Advanced Geometry: Unit 6 Review Learning Target 6.1: Use Pythagorean Theorem to identify and justify relationships in triangles and apply relationships in problems involving right triangles What does the Pythagorean Theorem say?

What are the two ways that you can use the Pythagorean Theorem?

Find the missing side of each triangle. Give answers in simplest radical form. a) b)

x

c)

x

d)

x

Determine if each set of measures can be the measures of the sides of a right triangle. a) 8, 11, 13 b) 16, 34, 30 c)

Solve the following word problems using the Pythagorean Theorem. Give answers in simplest radical form. Make a drawing and give units for your answer. a) A car drives 50 miles east and then 40 miles due north. How far is it from where it started?

b) Two boats leave the same dock at the same time, one traveling due north at a rate of 3 mph and the other due east at a rate of 4 mph. How many miles apart are the boats after 5 hours?

c) Susie is 1.4 meters tall. At a certain time her shadow is 2 meters long. What is the distance from the top of her head to the tip of her shadow? Round your answer to the nearest tenth.

What are the two types of special right triangles you learned about?

What is the rule for 45-45-90 triangles?

What are the two rules for 30-60-90 triangles?

Find the value of the variables. Give answers in simplest radical form. a) b)

c)

d)

e)

f)

x

y

g) Jana is cutting a square of material for a tablecloth. The table’s diagonal is 36 inches, but she wants the diagonal of the tablecloth to be 10 inches longer so that it will hang over the sides of the table. How long should the sides of her tablecloth be? Round your answer to the nearest tenth of an inch.

h) A skateboard ramp must be set up to rise 30° from the ground. If the height of the ramp is 8 feet, how long is the ramp?

Learning Target 6.2: Solve right triangles and application problems using trigonometric ratios What is the saying to help you remember your trig ratios?

When are trig ratios useful for solving problems? (Given what? Finding what?)

What always comes immediately after the trig ratio (sin, cos, tan) in an equation?

When do you use inverse trig ratios?

Solve for each variable. Round to the nearest tenth. a) b)

c)

d)

e)

f)

g)

h)

i)

Make a drawing and use trig ratios to solve the following problems. Round all answers to the nearest tenth. Include units on all answers. a) An eagle spotted a mouse 20 feet below at an angle of 42 degrees with the horizon. If the eagle flies along its line of sight, how far will it have to fly to reach its prey?

b) A lift chair at a ski resort has an angle of elevation of 28° and covers a total distance of 4640 feet to reach the top of the mountain. What is the horizontal distance covered by the ski lift?

c) An airplane which had taken off from an airport traveled a ground distance (horizontal) of 3,660 feet. What is the angle of elevation from the point of take-off to the point when the plane has traveled 4,150 feet through the air?

d) You are in a hot air balloon 600 feet in the air looking down at a friend taking your picture. Your friend is 1000 feet from a point directly under the balloon, and is holding the camera 6 feet above the ground. What is the angle of depression from the balloon to the camera?

e) A boy who is flying a kite lets out 300 feet of string which has an angle of elevation of 52°. The boy is holding the string 4 feet above the ground. Assuming that the string is stretched taut, find how high the kite is above ground.

f) A hiker whose eyes are 5.5 feet above ground stands 25 feet from the base of a redwood tree. She looks up at an angle of 71° to see the top of the tree. What is the height of the tree?

g) At 10:00am, a person observes a hot air balloon climbing vertically in the air from a point 300 meters away from the launch pad for the balloon. The angle of elevation to the top of the balloon at this time is 25o. At 10:02am, the person observes that the angle of elevation to the balloon is now 60o. What is the change in altitude for the balloon over the 2 minutes between the first and second observations?