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:
[tex]98ft+8ft=106ft[/tex]
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:
[tex]Tan(a)=\frac{opposite}{adjacent}[/tex]
The opposite side is the side of 106 ft
And the adjacent side is the side of 12ft
So the tangent is:
[tex]\tan (a)=\frac{106ft}{12ft}[/tex]
Solving the division:
[tex]\tan (a)=8.8333[/tex]
Finally, we use the inverse tangent to calculate a:
[tex]\begin{gathered} a=\tan ^{-1}(8.8333) \\ a=83.54 \end{gathered}[/tex]
Answer: The angle at which the bird flew with respect t the fence is 83.54°
