Please help me with my trig homework question. Its really hard and due today.

Question

Read and solve the word problem using the appropriate strategy: Pythagorean Theorem, Special Right Triangle Rules, or Right Triangle Trigonometry. 

A flagpole is propped on the east side corner of the roof of a building. The angle of depression from the top of the flagpole (Angle B) to a point on a neighboring building is 54 degrees. The angle of depression from the bottom of the flagpole (Angle A) to that same point on the building is 41 degrees. The distance from the edge of the building with the flagpole to the point on the neighboring building is 1660 feet (x). What is the height of the flagpole to the nearest tenth?  

height of flagpole = ___ feet  

image provided: https://ibb.co/c3h8LLm

Answer 1

Let d be the difference in the height of the two buildings.

Let y bet the height of the flagpole.

Let P be the point on the lower building.

x = the distance from the edge of the taller building to point P.

By opposite angles of parallel lines, the elevation angle from point P to the top of the flag pole is B°=54°.

tan(54°) = (y+d)/x --> y+d = 1660 tan(54°) = 2284.8 ft

By opposite angles of parallel lines, the elevation angle from point P to the bottom of the flag pole is A°=41°.

d/x = tan(41°) --> d = 1660tan(41°) = 1443 ft

y = 2284.8 -d = 2284.8-1443 = 841.8 ft.

height of flagpole = 841.8 feet  

Answer 2