Chapter 8.7, Problem 2WE

To determine

To find the angle of elevation of the sun if a vertical pole of 3 m tall casts a 4 m shadow.

Answer to Problem 2WE

Angle of elevation of the sun is ${37}^{\circ }$ .

Explanation of Solution

Given:

  

Calculation:

In triangle ABC,

  $\begin{array}{l}\tan x^{\circ }=\frac{AB}{BC}\\ \Rightarrow \tan x^{\circ }=\frac{3}{4}\\ \Rightarrow x^{\circ }={\tan }^{-1}\left(\frac{3}{4}\right)\\ \Rightarrow x^{\circ }={36.8698}^{\circ }\\ \Rightarrow x^{\circ }={37}^{\circ }\end{array}$

Hence height of the building is 32 m.