Question

A 1-mile stretch of road rises 450 feet. What is the angle of elevation of the road?(There are 5280 feet in a mile.) Round to the nearest degree, and enter the numberonly.

Answer 1

Let's take a look at the situation:

Using the law of sines

$\frac{5280}{\sin90}=\frac{450}{\sin\theta}$

Solving for theta,

$\begin{gathered} \frac{5280}{\sin90}=\frac{450}{\sin\theta} \\ \\ \rightarrow\frac{5280\sin\theta}{\sin90}=450\rightarrow5280\sin \theta=450\rightarrow\sin \theta=\frac{450}{5280} \\ \\ \theta=\sin ^{-1}(\frac{450}{5280})\Rightarrow\theta=4.88 \end{gathered}$

This way, the inclination of the road, round to the nearest degree is 5°