Question

Really need help solving thisIt’s trigonometry It’s from my ACT prep guide

Answer 1

We have the following configuration for this problem:

where y is the distance, in feet, Corey stepped back.

Then, we have:

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

And:

$\begin{gathered} \tan 41\degree=\frac{80}{x+y} \\ \\ x+y=\frac{80}{\tan 41\degree} \\ \\ y=\frac{80}{\tan 41\degree}-x \end{gathered}$

Now, using the first into the second equation, we obtain:

$\begin{gathered} y=\frac{80}{\tan41\degree}-\frac{80}{\tan 68\degree} \\ \\ y=59.71 \end{gathered}$

Therefore, Corey stepped back approximately 59.71 feet.