Question

1. find the angle of elevation on the following slopes. round to the nearest tenth.

a. a rise of 19 over a distance of 25
b. a rise of 15 and a run of 40
c. a vertical distance of 36 and a horizontal distance of 75

Explanation:

Step1: Recall the tangent - angle relationship

The slope of a line is given by the tangent of the angle of elevation. If the rise is $y$ and the run is $x$, then $\tan\theta=\frac{y}{x}$, where $\theta$ is the angle of elevation. We will use the inverse - tangent function $\theta = \tan^{- 1}(\frac{y}{x})$ to find the angle.

Step2a: For part a

Given $y = 19$ and $x = 25$. Then $\theta_a=\tan^{-1}(\frac{19}{25})$.
$\theta_a=\tan^{-1}(0.76)\approx37.2^{\circ}$

Step2b: For part b

Given $y = 15$ and $x = 40$. Then $\theta_b=\tan^{-1}(\frac{15}{40})=\tan^{-1}(0.375)$.
$\theta_b\approx20.6^{\circ}$

Step2c: For part c

Given $y = 36$ and $x = 75$. Then $\theta_c=\tan^{-1}(\frac{36}{75})=\tan^{-1}(0.48)$.
$\theta_c\approx25.6^{\circ}$

Answer:

a. $37.2^{\circ}$
b. $20.6^{\circ}$
c. $25.6^{\circ}$