Question

question 2 of 5 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 rounded to the nearest tenth of a foot? the shadow will be | feet.

Explanation:

Step1: Recall tangent - function in right - triangle

In a right - triangle formed by the light - pole, its shadow, and the line from the top of the pole to the end of the shadow, if the height of the pole is $h$ and the length of the shadow is $s$, and the angle of elevation of the sun is $\theta$, then $\tan\theta=\frac{h}{s}$.

Step2: Identify given values

We are given that $h = 20$ feet and $\theta = 26^{\circ}$. We need to find $s$.

Step3: Rearrange the formula to solve for $s$

From $\tan\theta=\frac{h}{s}$, we can get $s=\frac{h}{\tan\theta}$.

Step4: Substitute values and calculate

Substitute $h = 20$ and $\theta = 26^{\circ}$ into the formula. Since $\tan(26^{\circ})\approx0.4877$, then $s=\frac{20}{0.4877}\approx41$.

Answer:

41