Question

From the diagram below, if the tree is 61 ft. tall, and the angle of elevation from point B to the top of the tree is 29 °, find the distance that the tree is from point B. (Round to the nearest whole foot.)

Answer 1

So from the question, we get the height of the tree 61 ft and the angle of elevation in the B point 29°.

Now we going to use the trigonometric functions

We have the opposite side and an angle, and we going to find the adjacent side

The function that relates to all of this is tan

$\tan(B)=\frac{opposite}{adjacent}$$\tan(29°)=\frac{61}{adjacent}$

Solving for adjacent

$\begin{gathered} adjacent=\frac{61}{\tan(29°)} \\ adjacent=110.04 \end{gathered}$

Answer: 110 ft