Question

The ladder is resting on the top of the tree and is 8 ft from the bottom of the tree. It forms angle of elevation at 65o with the ground. What is height of the tree? Show your work. Round your answer to a nearest foot.

Answer 1

Given:

The ladder is resting on the top of the tree and is 8 ft from the bottom of the tree.

The angle of elevation is 65 degree.

This will form a right triangle,

The height is the tree is given by,

`\begin{gathered} \tan \theta=\frac{opposite\text{ side}}{\text{adjacent side}} \\ \tan 65^(\circ)=(h)/(8) \\ 2.14451=(h)/(8) \\ h=17.156 \end{gathered}`

Answer: the height of the tree is 17.2 ft.