Two office buildings are 51 meters apart. The height of the taller building is 207 meters. The angle of depression from the top of the taller building to the top of the shorter building is 15°. Find the height of the shorter building to the nearest meter.

The answer to your question is 17 m

Step-by-step explanation:

Data

distance = 51 m

height tallest building = 207 m

angle = 15°

Process

1. - Use trigonometric functions to find the difference in height of both buildings

Use tan Ф

tan Ф = Opposite side / Adjacent side

Solve for the adjacent side

Adjacent side = Opposite side / tan Ф

Substitution

Adjacent side = 51/tan 15

Adjacent side = 51 / 0.268

Adjacent side = 190.33 m

2. - Calculate the height of the short building by subtracting the height of the tall building and the difference of heights

Height of the small building = 207 - 190.33

= 16.7

≈ 17 m