Chapter 12.1, Problem 57HP

To determine

Write the function of the slope and the angle of elevation $\theta$ that the roof makes with the horizontal.

Answer to Problem 57HP

The function is $\tan \theta =\frac{2}{3}$ and the angle $\theta ={33.7}^{\circ }$ .

Explanation of Solution

Given: It is given in the question that a roof has a slope of $\frac{2}{3}$ .

Here, slope = $\frac{2}{3}$ .

Since, it is known that the tangent of an angle is the slope of the line formed by that angle.

So, the function is $\tan \theta =\frac{2}{3}$

Now,

  $\begin{array}{l}\tan \theta =\frac{2}{3}\\ \theta ={\tan }^{-1}(\frac{2}{3})\\ \theta ={33.7}^{\circ }\end{array}$