Solving for side lengths of right triangles

Diana works in a building that is 130 feet tall. She is outside, looking up at the building at an angle of 37° from her feet to the top of the building. If Diana walks forward and her angle looking to the top of the building changes to 40°, how much closer is she to the building? Round the answer to the nearest tenth of a foot.

17.6 ft

A 25-foot long ladder is propped against a wall at an angle of 18° with the wall. How high up the wall does the ladder reach? Round the answer to the nearest tenth of a foot.

23.8 ft

Use the diagram to complete the statements. The measure of angle L is _____. The trigonometric ratio that uses ∠M and LN to solve for NM is ____. The length of NM, to the nearest tenth, is approximately _____.

70°, Tangent, and 57.7

The measure of angle A is 15°, and the length of side BC is 8. What are the lengths of the other two sides, rounded to the nearest tenth?

AC = 29.9 AB = 30.9

A 25-foot long ladder is propped against a wall at an angle of 18° with the wall. Which diagram correctly represents this scenario?

B.

Kevin was asked to determine the length of side XZ. His work is shown. Which error did Kevin make?

He has the side lengths in the wrong place in the cosine ratio.

A building in a downtown business area casts a shadow that measures 88 meters along the ground. The straight-line distance from the top of the building to the end of the shadow it creates is at a 32° angle with the ground. What is the approximate height of the building? Round your answer to the nearest meter.

The building is ⇒ 55 meters high.

Which equation could be used to solve for the length of XY?

XY = 22\sin(41°)

Which equations could be used to solve for the unknown lengths of △ABC? Check all that apply.

sin(45°) = BC/9, cos(45°) = BC/9