1 Answer

Tamara · Answer 1 · 2023-02-16T08:14:07+0000

We have the following configuration for this problem:

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

Then, we have:

$\begin{gathered} \tan 68\degree=(80)/(x) \\ \\ x=(80)/(\tan 68\degree) \end{gathered}$

And:

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

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

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

Therefore, Corey stepped back approximately 59.71 feet.

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