Question

An owl is sitting on top of a tree that is 200 feet high. A mouse holding a cheese spots the owl on top of the tree at an angle of elevation of 32”. How far must the owl fly to get to the cheese? Round your answer to the nearest tenths

Answer 1

The next right triangle is formed:

x (in ft) represents the distance that the owl has to fly.

By definition,

`\sin (\text{angle)}=\frac{\text{ opposite side}}{\text{ hypotenuse}}`

From the picture,

`\sin (32^o)=(200)/(x)`

Solving for x:

`\begin{gathered} x=(200)/(\sin (32^o)) \\ x=(200)/(0.53) \\ x=377.4\text{ ft} \end{gathered}`