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
[tex]\tan (68^o)=\frac{\text{opposite}}{\text{adjacent}}[/tex][tex]\Rightarrow\tan (68^o)=\frac{\text{8}0}{\text{x}}[/tex]
We solve for x and get
[tex]\begin{gathered} \Rightarrow x\tan (68^o)=80 \\ \Rightarrow x=\frac{80}{\tan (68^o)} \end{gathered}[/tex]
since tan (68) = 2.475.., the above becomes
[tex]x=\frac{80}{2.75\ldots}=32.32[/tex]
Now, for angle 41 we have
[tex]\tan (41^o)=\frac{opposite}{\text{adjacent}}[/tex][tex]\tan (41^o)=\frac{80}{y}[/tex]
solving for y gives
[tex]y=\frac{80}{\tan (41^o)}[/tex]
since tan(41) = 0.869..., the above becomes
[tex]y=\frac{80}{0.869\ldots}[/tex][tex]\Rightarrow y=92.0295\ldots[/tex]
Therefore, the distance Corey has to step away from the tree to get a better view is (rounded to the nearest hundredth)
[tex]y-x=92.0295-32.322[/tex][tex]\boxed{y-x=59.71.}[/tex]
