Question

the builder of a parking garage wants to build a ramp at an angle of 12° that covers a horizontal span of 95 feet. how long will the actual ramp be? round your solution to four decimal places.

Explanation:

Step1: Identify the trigonometric relationship

We know the horizontal span (adjacent side to the angle) and we want to find the length of the ramp (hypotenuse). We use the cosine function $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, $\theta = 12^{\circ}$ and the adjacent side $x = 95$ feet. Let the length of the ramp be $l$. So, $\cos(12^{\circ})=\frac{95}{l}$.

Step2: Solve for the length of the ramp

We can re - arrange the formula $\cos(12^{\circ})=\frac{95}{l}$ to get $l=\frac{95}{\cos(12^{\circ})}$. We know that $\cos(12^{\circ})\approx0.9781$. Then $l=\frac{95}{0.9781}\approx97.1271$.

Answer:

$97.1271$