Chapter 8.7, Problem 11WE

To determine

To find: the angle of elevation of the road.

Answer to Problem 11WE

The angle of elevation of the road is $\simeq 14°$

Explanation of Solution

Given Information: A road is 1.6 km long and has an elevation of 400 m.

Formula used: The length of the road and elevation can be represented as a part of right angled triangle as shown in the figure below. Here, the angle of elevation is represented as B and the variables representing elevation and length of the road are a and b respectively.

  

The angle of elevation can be expressed as,

  $\begin{array}{l}\tan B=\frac{a}{b}\\ B={\tan }^{-1}\left(\frac{a}{b}\right)\end{array}$

Calculation: Consider the above figure. The elevation of the road is given as a=400 m and the length of the road is b=1.6 km

So, the angle of elevation can be calculated as

  $\begin{array}{c}B={\tan }^{-1}\left(\frac{400}{1600}\right)\\ ={\tan }^{-1}\left(0.25\right)\\ =14.03\\ \simeq 14°\end{array}$