The angle of elevation to the top of a building is 45 degrees. If you move 20 feet farther away, the angle of elevation to the top of the building becomes 30 degrees. What is the height of the building (in feet)?
+128474 Let d be the original distance to the building
Let h be the height of the building
Since the original angle of elevation is 45°, then d = h
So when we move 20 feet back we have that
tan 30° = d / [d + 20] rearrange as
[ d + 20] tan30° = d
d tan 30 + 20 tan 30° = d
20 tan 30° = d - dtan30°
20tan30° = d ( 1 - tan 30°)
[ 20tan30° ] / [ 1 - tan 30°] = d ≈ 27.32 ft = h
