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Simora [160]
3 years ago
9

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 pers

on’s eye level is \(5\) feet from the ground. What is the height of the lightpost to the nearest foot.

Mathematics
1 answer:
scoundrel [369]3 years ago
6 0

Answer:

The height of the lightpost is 33.008 feet

Step-by-step 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

\frac{Perpendicular}{Base}=Tan \theta \\\frac{DE}{CE}=tan 35^{\circ}\\\frac{DE}{40}=tan 35^{\circ}\\DE=40 \times 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

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