Chapter 4.8, Problem 18E

To determine

Tofind:The length of the shadow cast by a park statueif the height of thestatue is 12 feet and the sun is $20°$ above horizon.

Answer to Problem 18E

The length of the shadow cast by the park statue is $32.97$ feet.

Explanation of Solution

Given information:

The height of the park statue is 12 feet and the sun makes an angle of $20°$ with horizon.

Calculation:

Let’s the height of the park statue is $h$ . The sun makes an angle of $20°$ with horizon. So, the length of the shadow cast by the park statue is equal to the distance between the bottom of the park statue and the point at which the sun makes an angle.

Draw the diagram.

  

Calculate the length of the shadow.

  $\begin{array}{c}\tan 20°=\frac{12}{x}\\ x=\frac{12}{\tan 20°}\\ =\frac{12}{0.3639}\\ \approx 32.97\text{feet}\end{array}$

Therefore, the length of the shadow cast by the parkstatue is $32.97$ feet.