Question

The angle of elevation from a ball on a football field to the top of a 30-foot tall goal post is 16 degrees 42 minutes. How far is the football from the base of the goal post? Round to the nearest tenth of a foot

Answer 1

100.0 feet

Explanation:

You want to know the distance to a goalpost when the angle to the top of its 30 ft height is 16°42'.

Tangent

The tangent relation is ...

Tan = Opposite/Adjacent

Multiplying by Adjacent/Tan gives ...

Adjacent = Opposite/Tan

Application

In this problem, the distance to the goal can be modeled by the side "adjacent" to the acute angle 16°42' in a right triangle, and the "opposite" side will be the height of the goal.

adjacent = 30'/tan(16°42') ≈ 99.995 ft

Rounded to the nearest tenth, the distance to the goalpost is 100.0 feet.