Chapter 12.5, Problem 1P

To determine

Find the angle of elevation of sun when a tree of height 6.25 meter casts a shadow of 10.1 meter.

Answer to Problem 1P

The angle of elevation of Sun is $31.7°$ .

Explanation of Solution

Given information: The height of tree is 6.25 meter which casts a shadow of 10.1 meter.

Calculation: Consider that the height of the tree is (BC) equal to 6.25 meter and the shadow casted by sun is (AB) equal to 10.1 meter. Now if $\left(\theta \right)$ is the angle of elevation of the Sun then by trigonometric ratio in triangle assumed below,

  

  $\begin{array}{c}\tan \left(\theta \right)=\frac{BC}{AB}\\ \tan \left(\theta \right)=\frac{6.25}{10.1}\\ \theta ={\tan }^{-1}\left(\frac{6.25}{10.1}\right)\\ \theta =31.7°\end{array}$

Hence the angle of elevation of Sun is $31.7°$ .