1 Answer

Maydin · Answer 1 · 2023-11-08T04:50:20+0000

Answer:

Corey stepped 59.71 ft away

Step-by-step explanation:

The situation is sketched in the following diagram.

The distance from the foot of the tree is y and x for angles 41 and 68 degrees respectively.

Therefore, the distance Corey has to step away is y - x.

Now, from trigonometry, we know that

$\tan (68^o)=\frac{\text{opposite}}{\text{adjacent}}$
$\Rightarrow\tan (68^o)=\frac{\text{8}0}{\text{x}}$

We solve for x and get

$\begin{gathered} \Rightarrow x\tan (68^o)=80 \\ \Rightarrow x=(80)/(\tan (68^o)) \end{gathered}$

since tan (68) = 2.475.., the above becomes

$x=(80)/(2.75\ldots)=32.32$

Now, for angle 41 we have

$\tan (41^o)=\frac{opposite}{\text{adjacent}}$
$\tan (41^o)=(80)/(y)$

solving for y gives

$y=(80)/(\tan (41^o))$

since tan(41) = 0.869..., the above becomes

$y=(80)/(0.869\ldots)$
$\Rightarrow y=92.0295\ldots$

Therefore, the distance Corey has to step away from the tree to get a better view is (rounded to the nearest hundredth)

$\boxed{y-x=59.71.}$

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