Question

I need help answer and solving problem his This is a practice problem from my trigonometry prep guide

Answer 1

We have the following diagram

First, we find the distance from Corey to the tree (x). We use the trigonometric tangent identity:

$\begin{gathered} \tan 68=\frac{opposite}{adjacent} \\ \tan 68=\frac{80}{x} \end{gathered}$

And solve for x:

$x=\frac{80}{\tan 68}=32.32$

So, x = 32.32 ft

Now Corey moves back to watch the very same tree at an elevation angle of 41°. The tree has the same height, we find y:

$\begin{gathered} \tan 41=\frac{80}{y} \\ y=\frac{80}{\tan 41} \\ y=92.03 \end{gathered}$

This is y = 92.03 ft

We can know the distance Corey step back by subtracting both distances:

$92.03-32.32=59.71$

Answer: 59.71 ft