Answer:
14.3 ft
Explanation:
We can represent the situation as:
Now, we can relate the measure of the angle, the height x, and the distance 10 ft using the trigonometric function tangent as:
[tex]\begin{gathered} \tan 55=\frac{Opposite}{Adjacent} \\ \tan 55=\frac{x}{10} \end{gathered}[/tex]So, solving for x, we get:
[tex]\begin{gathered} 10\cdot\tan 55=10\cdot\frac{x}{10} \\ 10\cdot\tan 55=x \\ 10\cdot1.43=x \\ 14.3\text{ ft = x} \end{gathered}[/tex]Therefore, the height of the nest to the nearest tenth is 14.3 ft.
