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

Answer:

The buildings are 171.4 ft far apart.

Step-by-step 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

$\tan \theta =\frac{AB}{BC}$

$\tan 55^o=\frac{120 ft}{BC}$

$BC=120 ft\times \tan 55^o$

$BC=171.4 ft$

The buildings are 171.4 ft far apart.