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

`(5280)/(\sin90)=(450)/(\sin\theta)`

Solving for theta,

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

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