Chapter 14, Problem 14CPE

To determine

Tofind: the angle of elevation of the sun.

Answer to Problem 14CPE

The angle of elevation of the sun is ${\tan }^{-1}\frac{8}{5}$ .

Explanation of Solution

Given information:

A tree $5\text{m}$ tall casts a shadow $8\text{m}$ long.

Calculation: to find the angle of elevation of the sun, first draw the triangle for tree and its shadow,

Here the tree is $BC$ and shadow is $AB$ , and the angle is $C$ ,

$\begin{array}{l}\tan C=\frac{AB}{BC}\\ \tan C=\frac{8}{5}\text{ [substitute]}\\ C={\tan }^{-1}\frac{8}{5}\text{ [simplify]}\end{array}$

Thus, the angle of elevation of the sun is ${\tan }^{-1}\frac{8}{5}$ .