Question

A person is standing \(40\) ft from a light post and can see the top of the light at a \(35^\circ\) angle of elevation. The person’s eye level is \(5\) feet from the ground. What is the height of the lightpost to the nearest foot.

Answer 1

The height of the lightpost is 33.008 feet

Explanation:

Refer the attached figure

Distance between lamp post and person = AB = 40 feet

Height of person = BC = 5 feet

The angle of elevation = ∠DCE =35°

Height of light post = AD

AB=CE=40 feet

In ΔDCE

`(Perpendicular)/(Base)=Tan \theta \\(DE)/(CE)=tan 35^(\circ)\\(DE)/(40)=tan 35^(\circ)\\DE=40 * tan 35^(\circ)\\DE=28.008`

Height of light post = AD=DE+AE=28.008+5=33.008

Hence the height of the lightpost is 33.008 feet