We have the following diagram
First, we find the distance from Corey to the tree (x). We use the trigonometric tangent identity:
[tex]\begin{gathered} \tan 68=\frac{opposite}{adjacent} \\ \tan 68=\frac{80}{x} \end{gathered}[/tex]
And solve for x:
[tex]x=\frac{80}{\tan 68}=32.32[/tex]
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:
[tex]\begin{gathered} \tan 41=\frac{80}{y} \\ y=\frac{80}{\tan 41} \\ y=92.03 \end{gathered}[/tex]
This is y = 92.03 ft
We can know the distance Corey step back by subtracting both distances:
[tex]92.03-32.32=59.71[/tex]
Answer: 59.71 ft
