Two buildings are 60 meters apart. Find the height of the taller building

Question

The angle of depression from the top of the taller building to the top of the shorter building is 15 degrees. The height of the shorter building is 30.4 meters

Answer 1

draw a picture

the distance between the buildings, the distance from the top of the taller building to the top of the smaller building, and the horizontal distance from the top of the smaller building to part way up the taller building form a right triangle. the angle of depression is the same as the angle of elevation

tan=opposite/adjacent

tan15º=x/60 where x is the distance from the top of the smaller building to the top of the taller building

x=tan15º*60

x=(0.2679492)(60)

x=16.07695

this distance plus the height of the smaller building is the height of the taller building

30.4+16.07=46.47 meters is the height of the taller building