Question

tamara wants to calculate the height of a tree outside her home. using her clinometer, she measures the slope angle from 35 feet away from the base of the tree and gets an angle of 62°. Tamaras eye level is 5.5 feet above the ground

Answer 1

We can make a drawing to see better:

For Part A, we need the tangent function to find the height.

For Part B, the equation for the height of tree is:

$\begin{gathered} \text{height of tree}=heigth\text{ of Tamara + }35feet\cdot\tan 62 \\ \text{height of tr}ee=5.5+35\cdot\tan 62 \end{gathered}$

For Part C, the height of tree is:

$\begin{gathered} \text{height of tr}ee=5.5+35\cdot\tan 62 \\ \text{height of tre}e=5.5+35\cdot1.8807\approx71.3 \end{gathered}$

The height of tree is 71.3 ft.