Question

I need help with this practice problem, I am struggling to solve It’s from my trigonometry prep guide

Answer 1

Answer:

Corey stepped 59.71 ft away

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

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

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

$x=\frac{80}{2.75\ldots}=32.32$

Now, for angle 41 we have

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

solving for y gives

$y=\frac{80}{\tan (41^o)}$

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

$y=\frac{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)

$y-x=92.0295-32.322$$\boxed{y-x=59.71.}$