Chapter CSB1.11, Problem 8E

To determine

To find: The angle that the ramp makes with the highway.

Answer to Problem 8E

  $2°$

Explanation of Solution

Given information:

The end of an exit ramp from an interstate highway in 22 feet higher than the highway. The ramp is 630 feet long.

Calculation:

  

Let the angle made by the ramp with the highway be $x°$ .Let AB be the ramp and AC be the highway.

Using the sine ratio,

  $\begin{array}{l}\sin \angle A=\frac{\text{measure of leg opposite }\angle A}{\text{measure of the hypotenuse}}\\ \Rightarrow \sin x=\frac{22}{630}\\ \Rightarrow x={\sin }^{-1}\frac{22}{630}\\ \Rightarrow x=2.0012\end{array}$

The measure of $\angle A$ is about $2°$ .

Thus, the ramp makes an angle of $2°$ with the highway.