Question

14. A bird is perched on a 12 ft fence which is 8 ft from a 98 ft-wide highway. If the bird flies in a straight line and lands exactly at the oppo- site edge of the highway, at what angle did he fly with respect to the fence? (Note: This is not the angle of depression.)

Answer 1

The fence, the highway, and the path of the bird form a right triangle.

In the following image the legs of the right triangle are shown in red:

The leg at the bottom is equal to:

`98ft+8ft=106ft`

And the other leg is equal to 12 ft:

Now, we are asked for the angle at which the bird flew with respect to the fence. This angle is shown in green in the following image:

We will call the angle "a" for reference.

Now, we use the trigonometric function Tangent to find the angle:

`Tan(a)=(opposite)/(adjacent)`

The opposite side is the side of 106 ft

And the adjacent side is the side of 12ft

So the tangent is:

`\tan (a)=(106ft)/(12ft)`

Solving the division:

`\tan (a)=8.8333`

Finally, we use the inverse tangent to calculate a:

`\begin{gathered} a=\tan ^(-1)(8.8333) \\ a=83.54 \end{gathered}`

Answer: The angle at which the bird flew with respect t the fence is 83.54°