Chapter 8.7, Problem 1WE

To determine

To find the height of the building which casts a shadow of 21 m long and sun’s angle of elevation is ${57}^{\circ }$ .

Answer to Problem 1WE

32 m.

Explanation of Solution

Given:

  

Calculation:

In triangle ABC,

  $\begin{array}{l}\tan {57}^{\circ }=\frac{AC}{BC}\\ \Rightarrow \tan {57}^{\circ }=\frac{AC}{21}\\ \Rightarrow AC=21\cdot \tan {57}^{\circ }\\ \Rightarrow AC=32.3371\\ \Rightarrow AC\approx 32\end{array}$

Hence height of the building is 32 m.