What is the height of a hill when the angle of elevation to the top of the hill from a point is 50 degrees and is 30 degrees from a point 40 feet farther away from the base of the hill?

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 = (40 ft × tan 50° × tan 30°)/(tan 50° - tan 30°) ≈ 44.80 ft