Chapter 8.7, Problem 8WE

To determine

the height of the shorter building.

Answer to Problem 8WE

Height of the shorter building is 176 m.

Explanation of Solution

Given:

Distance between the buildings is 40 m and the height of the taller building is 185 m. Consequently, the angle of depression to the top of the shorter building is $13°$ .

Calculation:

By the ratio of sides from a right − angled triangle, we can write:

  $\begin{array}{l}\tan \theta =\frac{\text{Opposite side}}{\text{Adjacent side}},\\ \Rightarrow \tan 13°=\frac{185-x}{40},\\ \Rightarrow 0.2309=\frac{185-x}{40},\\ \Rightarrow 185-x=9,\\ \Rightarrow x=185-9,\\ \Rightarrow x=176\text{ m}\text{.}\end{array}$