Question

2.) the angle of elevation from a point 93.2 ft from the base of a tower to the top of the tower is 38.5°. find the height of the tower.

Explanation:

Step1: Recall tangent - function relation

We know that in a right - triangle formed by the tower, the ground, and the line of sight, $\tan\theta=\frac{opposite}{adjacent}$, where $\theta$ is the angle of elevation, the opposite side is the height of the tower ($h$), and the adjacent side is the distance from the base of the tower. Here, $\theta = 38.5^{\circ}$ and the adjacent side $x = 93.2$ ft.
So, $\tan(38.5^{\circ})=\frac{h}{93.2}$.

Step2: Solve for the height $h$

We can rewrite the equation as $h = 93.2\times\tan(38.5^{\circ})$.
We know that $\tan(38.5^{\circ})\approx0.795$.
Then $h=93.2\times0.795$.
$h = 93.2\times0.795=73.094\approx73.1$ ft.

Answer:

$73.1$ ft