Question

A student is standing 20 feet away from the base of a tree. He looks to the top of the tree at a 50°angle of elevation. His eyes are 5 feet above the ground. Using cos 50° 0.64, what is the heightof the tree to the nearest foot?

Answer 1

Given:

Base distance = 20 ft.

Angle = 50

Ground height = 5 ft

Find-:

The height of the tree

Explanation-:

The height of the tree

The height of the tree is:

`\text{ Height }=H+5\text{ ft}`

Value of H is:

In triangle ABC

`\begin{gathered} \text{ Angle }=50 \\ \\ \text{ Base }=20 \\ \\ \text{ Perpendicular }=H \end{gathered}`

Trignometry formula is:

`\tan\theta=\frac{\text{ Perpendicular}}{\text{ Base}}`

The value of "H" is:

`\begin{gathered} \tan50=(H)/(20) \\ \\ H=20*\tan50 \\ \\ H=20*1.19 \\ \\ H=23.83507 \\ \\ H\approx24 \end{gathered}`

So the height of the tree is:

`\begin{gathered} \text{ Height }=H+5 \\ \\ \text{ Height }=24+5 \\ \\ \text{ Height }=29\text{ feet} \end{gathered}`

Height of the tree is 29 feet.