Question 1 (Essay Worth 10 points) (05.01 MC)

Triangle XYZ was dilated by a scale factor of 2 to create triangle ACB and tan ∠X = 5 over 2 and 5 tenths.

Part A: Use complete sentences to explain the special relationship between the trigonometric ratios of triangles XYZ and ABC. You must show all work and calculations to receive full credit. (5 points)

Part B: Explain how to find the measures of segments AC and CB. You must show all work and calculations to receive full credit. (5 points)

Triangles XYZ and ACB; angles Y and C both measure 90 degrees, angles A and X are congruent.

Question 2 (Essay Worth 10 points)
(05.01 HC)

Use the image below to answer the following question. Find the value of sin x° and cos y°. What relationship do the ratios of sin x° and cos y° share?

A right triangle is shown with one leg measuring 8 and another leg measuring 6. The angle across from the leg measuring 6 is marked x degrees, and the angle across from the leg measuring 8 is marked y degrees.

Question 3 (Essay Worth 10 points)
(05.02 MC)

Quinn is flying a kite. The angle of elevation formed by the kite string and the ground is 40°, and the kite string forms a straight segment that is 100 feet long.

Explain how to find the distance between the ground and the kite. Include a description of the triangle you drew to help you solve, including the variables and measurements you assigned to each side and angle. Round your answer to the nearest foot.

Question 4 (Essay Worth 10 points)
(05.03 MC)

An observer (O) is located 900 feet from a building (B). The observer notices a helicopter (H) flying at a 49° angle of elevation from his line of sight. How high is the helicopter flying over the building? You must show all work and calculations to receive full credit.

A right triangle is shown with one leg measuring 900 and another leg measuring h, with an angle across from it measuring 49 degrees.