Name: ________________________ Date: __________

Quarter 3 MCA Review Packet Multiple Choice Identify the letter of the choice that best completes the statement or answers the question. ____

1. RU is an angle bisector. ∠RTU = 13x − 24, ∠TRS = 12x − 34, and ∠RUS = 92. Find m∠RSU . Is RU ⊥ TS ? R S T U

a. b. ____

63; No 65; No

c. d.

60; Yes 29; No

2. XW is an angle bisector. ∠WZX = 5x + 11, ∠ZXW = 6x − 10, and ∠XWZ = 91. Find m∠WXY . C

Y

X

W A Z

a. b. ____

40 35

c. d.

38 30

3. ZC is an altitude. ∠CYW = 9x + 38, ∠WZC = 17x . Find m∠WZC . Z

A X

W Y

a. b.

34 32

C

c. d.

1

18 31

Determine the relationship between the measures of the given angles. ____

4. ∠PTC, ∠VPT P 11 4

T

8 K

8 3

V

____

7

3 C

a. ∠PTC > ∠VPT b. ∠PTC < ∠VPT 5. ∠JCQ, ∠RCQ R

c.

∠PTC = ∠VPT

c.

∠JCQ = ∠RCQ

15 6 J

Q 10

4

12

4 C

Y 6

17 B

a. b.

∠JCQ > ∠RCQ ∠JCQ < ∠RCQ

Determine the relationship between the lengths of the given sides. ____

6. HB, BL R

H

111° U 35° 22° 22° 89° B

a. b.

HB > BL HB = BL

56°

78° L

c. d.

2

cannot be determined HB < BL

____

7. ZX , YX Z 48°

17°

X 42° C

46°

107° Y

98° D

a. b.

ZX < YX ZX = YX

c.

ZX > YX

Determine whether the given measures can be the lengths of the sides of a triangle. Write yes or no. Explain. ____

8. 3, 9, 10 a. Yes; the third side is the longest. b. No; the sum of the lengths of two sides is not greater than the third. c. No; the first side is not long enough. d. Yes; the sum of the lengths of any two sides is greater than the third. ____ 9. 9.2, 14.5, 17.1 a. Yes; the third side is the longest. b. No; the first side is not long enough. c. Yes; the sum of the lengths of any two sides is greater than the third. d. No; the sum of the lengths of two sides is not greater than the third. ____ 10. An isosceles triangle has a base 9.6 units long. If the congruent side lengths have measures to the first decimal place, what is the shortest possible length of the sides? a. 4.9 c. 4.7 b. 19.3 d. 9.7

3

____ 11. Find x, y, and z.

y z

x

6

15

a. x ≈ 13.7, y ≈ 31.5, z ≈ 37.5 b. x ≈ 37.5, y ≈ 13.7, z ≈ 31.5 ____ 12. Find x.

11

c. d.

x ≈ 31.5, y ≈ 37.5, z ≈ 13.7 x ≈ 13.7, y ≈ 31.5, z ≈ 37.5

c. d.

146 4 6

c. d.

1144 1594

11

x

10

a.

6

b. 16 ____ 13. Find x.

37 x

15

a. b.

22 2 286

4

Determine whether ∆QRS is a right triangle for the given vertices. Explain. ____ 14. Q(–6, –2), R(2, –5), S(–3, 6) a. no; QR = 73 , QS = 73 , RS =

146 ; QR2 + QS2 ≠ RS2 b. yes; QR = 73 , QS = 73 , RS = 146 ; QR2 + QS2 = RS2 c. yes; QR = 73 , QS = 73 , RS = 146 ; RS2 + QS2 = RQ2 d. no; QR = 73 , QS = 73 , RS = 146 ; RS2 + QS2 ≠ RQ2 ____ 15. Determine whether the set of numbers can be the measures of the sides of a right triangle. Then state whether they form a Pythagorean Triple. 10, 24, 26 a. no, no c. yes, yes b. no, yes d. yes, no ____ 16. The length of a diagonal of a square is 24 2 millimeters. Find the perimeter of the square. a. 576 millimeters c. 96 millimeters b. 96 2 millimeters d. 1152 millimeters ____ 17. Find x and y.

y

13.1

x°

x = 45°, y = 13.1

c.

x = 30°, y = 13.1 2

x = 30°, y = 13.1 ____ 18. Find x and y.

d.

x = 45°, y = 13.1 2

a. b.

x

60°

24

y

a.

x = 24 3, y = 24

c.

x = 24, y = 24 3

b.

x = 12 3, y = 12

d.

x = 12, y = 12 3

5

____ 19. Find x and y. x

60°

3

30°

y

a.

x = 1.5 3, y = 1.5

c.

x = 3, y = 3 3

x = 3 3, y = 3 d. x = 1.5, y = 1.5 3 ____ 20. Find the measure of each angle to the nearest tenth of a degree. cos Y = 0.5135 a. 30.9 c. 0.5135 b. 59.1 d. 27.2 ____ 21. Use the figure to find the trigonometric ratio below. Express the answer as a decimal rounded to the nearest ten-thousandth. b.

C

A AC = 5 5 , CB =

____ 22.

____ 23.

____ 24.

____ 25.

D

B

5 , AD = 11, CD = 2, DB = 1

cos B a. 2.2361 c. 0.4472 b. 0.9839 d. 0.8944 Dante is standing at horizontal ground level with the base of the Empire State Building in New York City. The angle formed by the ground and the line segment from his position to the top of the building is 48.4°. The height of the Empire State Building is 1472 feet. Find his distance from the Empire State Building to the nearest foot. a. 1307 c. 2217 b. 7.65 d. 1968 Lynn is standing at horizontal ground level with the base of the Sears Tower in Chicago. The angle formed by the ground and the line segment from her position to the top of the building is 15.7°. The height of the Sears Tower is 1450 feet. Find her distance from the Sears Tower to the nearest foot. a. 408 feet c. 5159 feet b. 7 feet d. 5358 feet A rocket ship is two miles above sea level when it begins to climb at a constant angle of 3.5° for the next 40 ground miles. About how far above sea level is the rocket ship after its climb? a. 2.4 miles c. 653.9 miles b. 4.4 miles d. 655.9 miles A space shuttle is one kilometer above sea level when it begins to climb at a constant angle of 3° for the next 80 ground kilometers. About how far above sea level is the space shuttle after its climb? a. 4.2 kilometers c. 79.9 kilometers b. 5.2 kilometers d. 80.9 kilometers

6

____ 26. A hot air balloon is one mile above sea level when it begins to climb at a constant angle of 4° for the next 50 ground miles. About how far above sea level is the hot air balloon after its climb? a. 2.5 miles c. 4.5 miles b. 3.5 miles d. 716.03 miles A landscaper is making a retaining wall to shore up the side of a hill. To ensure against collapse, the wall should make an angle 75° or less with the ground. ____ 27. If the wall is 25 feet, what is the height of the hill? a. 6.5 ft c. 25.9 ft b. 24.1 ft d. 93.3 ft ____ 28. If the wall is 15 feet, what is the height of the hill? a. 55.98 ft c. 14.49 ft b. 15.53 ft d. 3.88 ft ____ 29. How far from the base of the hill is the base of a 25-foot slanted wall? a. 6.5 ft c. 93.3 ft b. 24.1 ft d. 96.6 ft ____ 30. How far from the base of the hill is the base of a 15-foot slanted wall? a. 3.88 ft c. 55.98 ft b. 14.49 ft d. 57.96 ft ____ 31. A hiker stops to rest and sees a deer in the distance. If the hiker is 48 yards lower than the deer and the angle of elevation from the hiker to the deer is 15°, find the distance from the hiker to the deer. a. 18.21 yd c. 179.14 yd b. 49.69 yd d. 185.46 yd ____ 32. A dog chasing some birds in the woods got away from its owner. If the owner is 30 feet lower than the dog and the angle of elevation from the owner to the dog is 10°, find the distance from the owner to the dog. a. 19.47 ft c. 170.14 ft b. 30.46 ft d. 172.76 ft ____ 33. A bird watcher spied a woodpecker. The bird watcher is 40 yards lower than the woodpecker. The distance from the bird watcher to the woodpecker is 175 yards. What is the angle of elevation? a. 12.9° c. 76.8° b. 13.2° d. 77.1° ____ 34. Two horses are observed by a hang glider 80 meters above a meadow. The angles of depression are 10.4° and 8°. How far apart are the horses? a. 133.3 m c. 569.2 m b. 435.9 m d. 1005.1 m ____ 35. A traffic helicopter pilot 60 meters above the road spotted two antique cars. The angles of depression are 10.2° and 8.7°. How far apart are the cars? a. 58.6 m c. 333.5 m b. 392.1 m d. 725.6 m ____ 36. Two cabins are observed by a ranger in a 60 feet tower above a park. The angles of depression are 11.6° and 9.4°. How far apart are the cabins? a. 70.1 ft c. 362.4 ft b. 292.3 ft d. 654.7 ft ____ 37. Two swimmers are observed by a lifeguard in a 30 feet tower above the water. The angles of depression are 12.7° and 14.5°. How far apart are the swimmers? a. 249.1 ft c. 116.0 ft b. 133.1 ft d. 17.1 ft 7

____ 38. After flying at an altitude of 600 meters, a hot air balloon starts to descend when its ground distance from the landing pad is 10 kilometers. What is the angle of depression for this part of the flight? a. 0.95° c. 86.57° b. 3.43° d. 89.05° ____ 39. A water slide is 400 yards long with a vertical drop of 36.3 yards. Find the angle of depression of the slide. a. 5.2° c. 436.3° b. 84.8° d. 363.7° ____ 40. A tubing run is 150 yards long with a vertical drop of 21.6 yards. Find the angle of depression of the run. a. 8.2° c. 81.7° b. 8.3° d. 81.8° Essay 41. Carla, Dani, and Ellis are practicing with a giant slingshot. Carla is standing at point C and Dani is standing at point D. Each of them is holding the handle for one end of the slingshot. Ellis is pulling back the middle of the slingshot, from which a ball will be released. Ellis is standing at point E, equidistant from Carla and Dani. When Ellis releases the ball from the slingshot, it will travel through point K. Prove that when Ellis’s ball goes through point K, it will be at the midpoint between Carla and Dani. E

C

K

D

8

ID: A

Quarter 3 MCA Review Packet Answer Section MULTIPLE CHOICE 1. ANS: A If RU is an angle bisector, the two angles of vertex R are equal. Also, the measures of the angles of every triangle add up to 180. DIF: Average OBJ: 5-1.2 Identify and use angle bisectors in triangles. STO: NCTM GM.1, NCTM GM.1a TOP: Identify and use angle bisectors in triangles. KEY: Angle Bisectors, Triangles MSC: 1998 Lesson 5-1 NOT: /A/ Correct! /B/ Check your math. /C/ Check your math. /D/ Determine the measures of which angles have to add up to 180. 2. ANS: C If XW is an angle bisector, the two angles of vertex X are equal. Also, the measures of the angles of every triangle add up to 180. DIF: Average OBJ: 5-1.2 Identify and use angle bisectors in triangles. STO: NCTM GM.1, NCTM GM.1a TOP: Identify and use angle bisectors in triangles. KEY: Angle Bisectors, Triangles MSC: 1998 Lesson 5-1 NOT: /A/ What two angles have the same measure? /B/ Check your math. /C/ Correct! /D/ Which angle measures add up to 180? 3. ANS: A If ZC is an altitude, m∠YCZ = 90. Also, the measures of the angles of every triangle add up to 180. DIF: Average OBJ: 5-1.4 Identify and use altitudes in triangles. TOP: Identify and use altitudes in triangles. KEY: Altitudes, Triangles MSC: 1998 Lesson 5-1 NOT: /A/ Correct! /B/ Which angle measures add up to 180?/C/ Which angles must measure 90°? /D/ Check your math. 4. ANS: B The measures of the sides opposite the angles given are compared. The longer the side, the larger its angle. DIF: OBJ: STO: TOP: KEY: NOT:

Average 5-2.1 Recognize and apply properties of inequalities to the measures of angles of a triangle. NCTM AL.2, NCTM AL.2b Recognize and apply properties of inequalities to the measures of angles of a triangle. Properties of Inequality, Triangles MSC: 1998 Lesson 5-4 /A/ Check the sides opposite the angles. /B/ Correct! /C/ Check the sides opposite the angles.

1

ID: A 5. ANS: C Different names for the same angle. DIF: Average OBJ: 5-2.1 Recognize and apply properties of inequalities to the measures of angles of a triangle. STO: NCTM AL.2, NCTM AL.2b TOP: Recognize and apply properties of inequalities to the measures of angles of a triangle. KEY: Properties of Inequality, Triangles MSC: 1998 Lesson 5-4 NOT: /A/ Check the sides opposite the angles. /B/ Check the sides opposite the angles. /C/Correct! 6. ANS: C The measures of the angles opposite the sides given are compared. The larger the angle, the longer its side. DIF: Average OBJ: 5-2.2 Recognize and apply properties of inequalities to the relationships between angles and sides of a triangle. STO: NCTM RP.1 TOP: Recognize and apply properties of inequalities to the relationships between angles and sides of a triangle. KEY: Properties of Inequality, Triangles MSC: 1998 Lesson 5-4 NOT: /A/ Check the angles opposite the sides. /B/ Are the angles in the same or congruent triangles? /C/Correct!/D/ Check the angles opposite the sides. 7. ANS: C The measures of the angles opposite the sides given are compared. The larger the angle, the longer its side. DIF: Average OBJ: 5-2.2 Recognize and apply properties of inequalities to the relationships between angles and sides of a triangle. STO: NCTM RP.1 TOP: Recognize and apply properties of inequalities to the relationships between angles and sides of a triangle. KEY: Properties of Inequality, Triangles MSC: 1998 Lesson 5-4 NOT: /A/ Check the angles opposite the sides. /B/ Check the angles opposite the sides./C/ Correct! 8. ANS: D The sum of the lengths of any two sides must be greater than the third. DIF: Basic OBJ: 5-4.1 Apply the Triangle Inequality Theorem. STO: NCTM GM.2, NCTM GM.2a TOP: Apply the Triangle Inequality Theorem. KEY: Triangles Inequality Theorem MSC: 1998 Lesson 5-5 NOT: /A/ Did you check all the sums? /B/ Add two sides and compare to the third. /C/ Add two sides and compare to the third./D/ Correct! 9. ANS: C The sum of the lengths of any two sides must be greater than the third. DIF: Average OBJ: 5-4.1 Apply the Triangle Inequality Theorem. STO: NCTM GM.2, NCTM GM.2a TOP: Apply the Triangle Inequality Theorem. KEY: Triangles Inequality Theorem MSC: 1998 Lesson 5-5 NOT: /A/ Did you check all the sums? /B/ Add two sides and compare to the third. /C/ Correct! /D/ Add two sides and compare to the third.

2

ID: A 10. ANS: A The sum of the lengths of any two sides must be greater than the third. DIF: Average OBJ: 5-4.2 Determine the shortest distance between a point and a line. STO: NCTM AL.2, NCTM AL.2b, NCTM GM.1 TOP: Determine the shortest distance between a point and a line. KEY: Distance, Distance Between a Point and a Line MSC: 1998 Lesson 5-5 NOT: /A/ Correct! /B/ Would both sides have to be longer than the base?/C/ Is the sum of the two sides longer than the base? /D/ Is that the shortest possible length? 11. ANS: A The altitude is the geometric mean between the measures of the two segments of the hypotenuse. DIF: Average OBJ: 7-1.2 Solve problems involving relationships between parts of a triangle and the altitude to its hypotenuse. STO: NCTM GM.1, NCTM GM.1b TOP: Solve problems involving relationships between parts of a triangle and the altitude to its hypotenuse. KEY: Triangles, Altitudes, Hypotenuse MSC: 1998 Lesson 8-1 NOT: /A/ Correct! /B/ What is the value of x? /C/ What is the value of y? /D/ How do you find the geometric mean? 12. ANS: D Divide the large triangle into two right triangles. Which side is the hypotenuse? Which sides are the legs? Substitute the values into the Pythagorean Theorem to solve for the missing variable. DIF: Basic OBJ: 7-2.1 Use the Pythagorean Theorem. STO: NCTM GM.1, NCTM GM.1b TOP: Use the Pythagorean Theorem. KEY: Pythagorean Theorem MSC: 1998 Lesson 8-1 NOT: /A/ Remember to square the numbers. /B/ Which side is the hypotenuse?/C/ Which side is the hypotenuse? /D/ Correct! 13. ANS: B The sum of the squares of the two sides is equal to the square of the hypotenuse. DIF: Basic OBJ: 7-2.1 Use the Pythagorean Theorem. STO: NCTM GM.1, NCTM GM.1b TOP: Use the Pythagorean Theorem. KEY: Pythagorean Theorem MSC: 1998 Lesson 8-1 NOT: /A/ Remember to square the numbers./B/ Correct! /C/ Remember to find the square root. /D/ Which side is the hypotenuse? 14. ANS: B Use the distance formula to determine the lengths of the sides. If the sum of the squares of the two shorter sides is equal to the square of the third side, the triangle is a right triangle. DIF: Average OBJ: 7-2.2 Use the converse of the Pythagorean Theorem. STO: NCTM GM.1, NCTM GM.1b TOP: Use the converse of the Pythagorean Theorem. KEY: Converse of Pythagorean Theorem MSC: 1998 Lesson 8-1 NOT: /A/ What is the converse of the Pythagorean Theorem? /B/ Correct! /C/ Check the Pythagorean Theorem. /D/ Check the Pythagorean Theorem.

3

ID: A 15. ANS: C Substitute the values into the Pythagorean Theorem to determine if the sides form a right triangle. The largest value is c. If the numbers are whole numbers, then the numbers form a Pythagorean Triple. DIF: Basic OBJ: 7-2.3 Determine whether sets of measures form a Pythagorean triple. STO: NCTM GM.1, NCTM GM.1d TOP: Determine whether sets of measures form a Pythagorean triple. KEY: Pythagorean Triples MSC: 1998 Lesson 8-1 NOT: /A/ Is the sum of the two smaller sides greater than the length of the third side? /B/ Do the three sides form a triangle?/C/ Correct! /D/ Try the Pythagorean Theorem again. 16. ANS: C To find the leg of a 45-45-90 triangle when the hypotenuse is given, divide the hypotenuse by 2 . To find the perimeter of the square, find the sum of all the sides. DIF: Average OBJ: 7-3.1 Use properties of 45º-45º-90º triangles. STO: NCTM GM.1, NCTM GM.1d TOP: Use properties of 45º-45º-90º triangles. KEY: Triangles, 45-45-90 Triangles MSC: 1998 Lesson 8-2 NOT: /A/ This is the area, not the perimeter of the square. /B/ Is the number given the length of a side or the diagonal?/C/ Correct! /D/ Before the perimeter can be found, first find the length of each side. 17. ANS: D The length of the hypotenuse is equal to the length of a leg times 2 . The diagonal of a square bisects the angle. DIF: Basic OBJ: 7-3.1 Use properties of 45º-45º-90º triangles. STO: NCTM GM.1, NCTM GM.1d TOP: Use properties of 45º-45º-90º triangles. KEY: Triangles, 45-45-90 Triangles MSC: 1998 Lesson 8-2 NOT: /A/ Multiply by the square root of two to find the length of the hypotenuse. /B/ Check the length of the hypotenuse and the size of the angle./C/ The diagonal of a square bisects the angle. /D/ Correct! 18. ANS: D The shorter leg is half the length of the hypotenuse. The longer leg is 3 times the length of the shorter leg. DIF: Basic OBJ: 7-3.2 Use properties of 30º-60º-90º triangles. STO: NCTM GM.1, NCTM GM.1d TOP: Use properties of 30º-60º-90º triangles. KEY: Triangles, 30-60-90 Triangles MSC: 1998 Lesson 8-2 NOT: /A/ How do you find the length of the side opposite the 60° angle?/B/ Switch the x and y values. /C/ How do you find the length of the side opposite the 30° angle? /D/ Correct! 19. ANS: D The shorter leg is half the length of the hypotenuse. The longer leg 3 times the length of the shorter leg. DIF: Average OBJ: 7-3.2 Use properties of 30º-60º-90º triangles. STO: NCTM GM.1, NCTM GM.1d TOP: Use properties of 30º-60º-90º triangles. KEY: Triangles, 30-60-90 Triangles MSC: 1998 Lesson 8-2 NOT: /A/ Switch the x and y values. /B/ How do you find the length of the side opposite the 60 degree angle?/C/ How do you find the length of the side opposite the 30 degree angle? /D/ Correct!

4

ID: A 20. ANS: B In trigonometry, you can find the measure of an angle by using the inverse of sine, cosine, or tangent. DIF: Basic OBJ: 7-4.1 Find trigonometric ratios using right triangles. STO: NCTM GM.1, NCTM GM.1d TOP: Find trigonometric ratios using right triangles. KEY: Trigonometric Ratios, Right Triangles MSC: 1998 Lesson 8-3 NOT: /A/ Which trigonometric ratio should be used? /B/ Correct! /C/ This is the ratio not the angle./D/ Which trigonometric ratio should be used? 21. ANS: C Determine the ratio associated with the given trigonometric term. Divide the numerator by the denominator. DIF: Average OBJ: 7-4.1 Find trigonometric ratios using right triangles. STO: NCTM GM.1, NCTM GM.1d TOP: Find trigonometric ratios using right triangles. KEY: Trigonometric Ratios, Right Triangles MSC: 1998 Lesson 8-3 NOT: /A/ Check the setup of the ratio./B/ Which trigonometric ratio are you asked to find? /C/ Correct! /D/ Which trigonometric ratio are you asked to find? 22. ANS: A Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer. DIF: Basic OBJ: 7-4.2 Solve problems using trigonometric ratios. STO: NCTM GM.1, NCTM GM.1d TOP: Solve problems using trigonometric ratios. KEY: Trigonometric Ratios, Solve Problems MSC: 1998 Lesson 8-3 NOT: /A/ Correct! /B/ Check the trigonometric ratio. /C/ Which trigonometric ratio should be used? /D/ Which trigonometric ratio should be used? 23. ANS: C Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer. DIF: Average OBJ: 7-4.2 Solve problems using trigonometric ratios. STO: NCTM GM.1, NCTM GM.1d TOP: Solve problems using trigonometric ratios. KEY: Trigonometric Ratios, Solve Problems MSC: 1998 Lesson 8-3 NOT: /A/ Check the trigonometric ratio. /B/ Which trigonometric ratio should be used? /C/ Correct! /D/ Which trigonometric ratio should be used? 24. ANS: B Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer. DIF: Average OBJ: 7-4.2 Solve problems using trigonometric ratios. STO: NCTM GM.1, NCTM GM.1d TOP: Solve problems using trigonometric ratios. KEY: Trigonometric Ratios, Solve Problems MSC: 1998 Lesson 8-3 NOT: /A/ Remember to include the initial height of two miles. /B/ Correct! /C/ Which trigonometric ratio should be used? /D/ Which trigonometric ratio should be used?

5

ID: A 25. ANS: B Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer. DIF: Average OBJ: 7-4.2 Solve problems using trigonometric ratios. STO: NCTM GM.1, NCTM GM.1d TOP: Solve problems using trigonometric ratios. KEY: Trigonometric Ratios, Solve Problems MSC: 1998 Lesson 8-3 NOT: /A/ Remember to include the initial height of one kilometer. /B/ Correct! /C/ Which trigonometric ratio should be used? /D/ Which trigonometric ratio should be used? 26. ANS: C Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer. DIF: Basic OBJ: 7-4.2 Solve problems using trigonometric ratios. STO: NCTM GM.1, NCTM GM.1d TOP: Solve problems using trigonometric ratios. KEY: Trigonometric Ratios, Solve Problems MSC: 1998 Lesson 8-3 NOT: /A/ Do not subtract the initial height of the balloon. /B/ Remember to include the initial height of one mile. /C/ Correct! /D/ Which trigonometric ratio should be used? 27. ANS: B Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer. DIF: Basic OBJ: 7-4.2 Solve problems using trigonometric ratios. STO: NCTM GM.1, NCTM GM.1d TOP: Solve problems using trigonometric ratios. KEY: Trigonometric Ratios, Solve Problems MSC: 1998 Lesson 8-3 NOT: /A/ Do not use the cosine ratio. /B/ Correct! /C/ Check the setup of the ratio. /D/ Do not use the tangent ratio. 28. ANS: C Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer. DIF: Basic OBJ: 7-4.2 Solve problems using trigonometric ratios. STO: NCTM GM.1, NCTM GM.1d TOP: Solve problems using trigonometric ratios. KEY: Trigonometric Ratios, Solve Problems MSC: 1998 Lesson 8-3 NOT: /A/ Do not use the tangent ratio. /B/ What is the sine ratio? /C/ Correct! /D/ Do not use the cosine ratio. 29. ANS: A Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer. DIF: STO: KEY: NOT: ratio?

Average OBJ: 7-4.2 Solve problems using trigonometric ratios. NCTM GM.1, NCTM GM.1d TOP: Solve problems using trigonometric ratios. Trigonometric Ratios, Solve Problems MSC: 1998 Lesson 8-3 /A/ Correct! /B/ Do not use the sine ratio. /C/ Do not use the tangent ratio. /D/ What is the cosine

6

ID: A 30. ANS: A Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer. DIF: Average OBJ: 7-4.2 Solve problems using trigonometric ratios. STO: NCTM GM.1, NCTM GM.1d TOP: Solve problems using trigonometric ratios. KEY: Trigonometric Ratios, Solve Problems MSC: 1998 Lesson 8-3 NOT: /A/ Correct! /B/ Do not use the sine ratio. /C/ Do not use the tangent ratio. /D/ What is the cosine ratio? 31. ANS: D Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer. DIF: Average OBJ: 7-5.1 Solve problems involving angles of elevation. STO: NCTM GM.1, NCTM GM.1d TOP: Solve problems involving angles of elevation. KEY: Angle of Elevation MSC: 1998 Lesson 8-4 NOT: /A/ Do not use inverse sine to solve. /B/ Do not use the cosine ratio. /C/ Do not use the tangent ratio. /D/ Correct! 32. ANS: D Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer. DIF: Average OBJ: 7-5.1 Solve problems involving angles of elevation. STO: NCTM GM.1, NCTM GM.1d TOP: Solve problems involving angles of elevation. KEY: Angle of Elevation MSC: 1998 Lesson 8-4 NOT: /A/ Do not use inverse sine to solve. /B/ Do not use the cosine ratio. /C/ Do not use the tangent ratio. /D/ Correct! 33. ANS: B Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer. DIF: Average OBJ: 7-5.1 Solve problems involving angles of elevation. STO: NCTM GM.1, NCTM GM.1d TOP: Solve problems involving angles of elevation. KEY: Angle of Elevation MSC: 1998 Lesson 8-4 NOT: /A/ Do not use the tangent ratio. /B/ Correct! /C/ Do not use the cosine ratio. /D/ Do not use the tangent ratio. 34. ANS: A Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer. DIF: Average OBJ: 7-5.2 Solve problems involving angles of depression. STO: NCTM GM.1, NCTM GM.1d TOP: Solve problems involving angles of depression. KEY: Angle of Depression MSC: 1998 Lesson 8-4 NOT: /A/ Correct! /B/ This is the horizontal distance from one horse to the hang glider. /C/ This is the horizontal distance from one horse to the hang glider. /D/ Subtract rather than add the distances.

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ID: A 35. ANS: A Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer. DIF: Average OBJ: 7-5.2 Solve problems involving angles of depression. STO: NCTM GM.1, NCTM GM.1d TOP: Solve problems involving angles of depression. KEY: Angle of Depression MSC: 1998 Lesson 8-4 NOT: /A/ Correct! /B/ This is the horizontal distance from one car to the helicopter. /C/ This is the horizontal distance from one car to the helicopter. /D/ Subtract rather than add the distances. 36. ANS: A Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer. DIF: Average OBJ: 7-5.2 Solve problems involving angles of depression. STO: NCTM GM.1, NCTM GM.1d TOP: Solve problems involving angles of depression. KEY: Angle of Depression MSC: 1998 Lesson 8-4 NOT: /A/ Correct! /B/ This is the horizontal distance from the tower to a cabin. /C/ This is the horizontal distance from the tower to a cabin. /D/ Subtract rather than add the distances. 37. ANS: D Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer. DIF: Average OBJ: 7-5.2 Solve problems involving angles of depression. STO: NCTM GM.1, NCTM GM.1d TOP: Solve problems involving angles of depression. KEY: Angle of Depression MSC: 1998 Lesson 8-4 NOT: /A/ Do not add the distances together. /B/ This is the ground distance from one swimmer to the tower. /C/ This is the ground distance from one swimmer to the tower. /D/ Correct! 38. ANS: B Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer. DIF: Average OBJ: 7-5.2 Solve problems involving angles of depression. STO: NCTM GM.1, NCTM GM.1d TOP: Solve problems involving angles of depression. KEY: Angle of Depression MSC: 1998 Lesson 8-4 NOT: /A/ Remember to convert km to m. /B/ Correct! /C/ Remember to convert km to m. /D/ Check the ratio. 39. ANS: A Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer. DIF: Average OBJ: 7-5.2 Solve problems involving angles of depression. STO: NCTM GM.1, NCTM GM.1d TOP: Solve problems involving angles of depression. KEY: Angle of Depression MSC: 1998 Lesson 8-4 NOT: /A/ Correct! /B/ Do not use the cosine ratio. /C/ Do not add together the numbers given. /D/ Do not subtract the numbers given.

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ID: A 40. ANS: B Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the answer. DIF: Average OBJ: 7-5.2 Solve problems involving angles of depression. STO: NCTM GM.1, NCTM GM.1d TOP: Solve problems involving angles of depression. KEY: Angle of Depression MSC: 1998 Lesson 8-4 NOT: /A/ Do not use the tangent ratio. /B/ Correct! /C/ Do not use the cosine ratio. /D/ Do not use the tangent ratio.

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ID: A

ESSAY 41. ANS: Since Ellis is equidistant from Carla and Dani, EC and ED are congruent and ∆ECD is an isosceles triangle. According to the Isosceles Triangle Theorem, ∠C and ∠D are also congruent. EK is perpendicular to CD, so ∠EKC and ∠EKD are both right angles and congruent. Two corresponding angles and the corresponding nonincluded sides are congruent (AAS Theorem), so ∆EKC and ∆EKD are congruent triangles. Since these triangles are congruent, the corresponding sides CK and DK are congruent and have equal lengths; therefore when Ellis’s ball crosses at point K it will be at the midpoint between Carla and Dani. Assessment Rubric Level 3 Superior *Shows thorough understanding of concepts. *Uses appropriate strategies. *Computation is correct. *Written explanation is exemplary. *Diagram/table/chart is accurate (as applicable). *Goes beyond requirements of problem. Level 2 Satisfactory *Shows understanding of concepts. *Uses appropriate strategies. *Computation is mostly correct. *Written explanation is effective. *Diagram/table/chart is mostly accurate (as applicable). *Satisfies all requirements of problem. Level 1 Nearly Satisfactory *Shows understanding of most concepts. *May not use appropriate strategies. *Computation is mostly correct. *Written explanation is satisfactory. *Diagram/table/chart is mostly accurate (as applicable). *Satisfies most of the requirements of problem. Level 0 Unsatisfactory *Shows little or no understanding of the concept. *May not use appropriate strategies. *Computation is incorrect. *Written explanation is not satisfactory. *Diagram/table/chart is not accurate (as applicable). *Does not satisfy requirements of problem. DIF: Advanced OBJ: 7-8.1 Solve problems and show solutions. STO: NCTM GM.1, NCTM GM.1a, NCTM ME.1 TOP: Solve problems and show solutions. KEY: Solve Problems, Show Solutions

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Quarter 3 MCA Review Packet [Answer Strip] C _____ 7.

ID: A A 11. _____

B _____ 4.

B 14. _____

C 15. _____ A _____ 1.

C _____ 5. C 16. _____ D _____ 8. D 17. _____ C _____ 2.

D 12. _____ C _____ 9.

A 10. _____ C _____ 6. A _____ 3. B 13. _____ D 18. _____

Quarter 3 MCA Review Packet [Answer Strip] D 19. _____

C 26. _____

B 38. _____

A 39. _____

B 27. _____

B 20. _____

C 28. _____

A 29. _____ C 21. _____ A 30. _____

D 31. _____

D 32. _____

A 22. _____

B 33. _____

A 34. _____ C 23. _____ A 35. _____ B 24. _____ A 36. _____ B 25. _____ D 37. _____

B 40. _____

ID: A

Name: ________________________ Class: ___________________ Date: __________ MULTIPLE CHOICE 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40.

A B C D E A B C D E A B C D E A B C D E A B C D E A B C D E A B C D E A B C D E A B C D E A B C D E A B C D E A B C D E A B C D E A B C D E A B C D E A B C D E A B C D E A B C D E A B C D E A B C D E A B C D E A B C D E A B C D E A B C D E A B C D E A B C D E A B C D E A B C D E A B C D E A B C D E A B C D E A B C D E A B C D E A B C D E A B C D E A B C D E A B C D E A B C D E A B C D E A B C D E

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ID: A