Question

from a window 24 feet above the ground, the angle of elevation to the top of another building is 38 degrees. The distance between the buildings 63 feet. Find the height of the building to the nearest tenth of a foot.

Answer 1

The height of the building is
`73.2\ ft`

Explanation:

see the attached figure to better understand the problem

we know that

In the right triangle ABC

`tan(38\°)=(BC)/(AB)`

we have

`AB=63\ ft`

substitute and solve for BC

`tan(38\°)=(BC)/(63)`

`BC=(63)tan(38\°)=49.2\ ft`

Find the height of the building

The height of the building (h) is equal to

`h=BC+24=49.2+24=73.2\ ft`