What is the approximate height of a building when the angle of elevation at the top of a building is 34 degrees and at a point 80 feet closer the angle of elevation is 45 degrees?

Answer 1

It can be shown that:

• height = (d tan α tan β)/(tan α - tan β)

where:

• α is the angle closest to the object
• β is the angle further away from the object
• d is the distance from the point of angle α to the point of angle β

Thus:

height = (80 ft × tan 45° × tan 34°)/(tan 45° - tan 34°) ≈ 165.78 ft

Answer 2

It is approx 165.8 feet.