Question

The angle of depression from the top of a 320 foot office building to the top of a 200 foot office building is 55 degrees. How far apart are the buildings?

Answer 1

The buildings are 171.4 ft far apart.

Explanation:

Height of the of the building-1 = 320 ft

Height of the of the building-2 = 200 ft

Angle of depression from building-1 to to the top of building-2 = θ = 55°

In figure attached, ABC

AB = 320 ft - 200 ft = 120 ft

BC = Distance between the buildings

`\theta =\angle ABC = 55^o`

In ΔABC

`\tan \theta =(AB)/(BC)`

`\tan 55^o=(120 ft)/(BC)`

`BC=120 ft* \tan 55^o`

`BC=171.4 ft`

The buildings are 171.4 ft far apart.