Question

select the correct answer from the drop - down menu. when the angle of elevation of the sun from the ground is 25°, how long is the shadow of a 20 - foot light pole? round your answer to the nearest tenth of a foot. the shadow will be feet. 9.3 feet 42.9 feet 47.3 feet 22.1 feet

Explanation:

Step1: Recall tangent - function relation

We know that in a right - triangle formed by the light pole, its shadow, and the sunlight ray, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, the height of the light pole is the opposite side and the length of the shadow is the adjacent side with respect to the angle of elevation of the sun. Let the height of the light pole $h = 20$ feet, the angle of elevation of the sun $\theta=25^{\circ}$, and the length of the shadow be $x$. Then $\tan\theta=\tan(25^{\circ})=\frac{h}{x}$.

Step2: Solve for $x$

We can re - arrange the formula $\tan(25^{\circ})=\frac{20}{x}$ to get $x = \frac{20}{\tan(25^{\circ})}$. Since $\tan(25^{\circ})\approx0.4663$, then $x=\frac{20}{0.4663}\approx42.9$ feet.

Answer:

42.9 feet