Question

question 5 of 16. step 1 of 1 the builder of a parking garage wants to build a ramp at an angle of 18° that covers a horizontal span of 45 feet. how long will the actual ramp be? round your solution to four decimal places. answer 4/10 correct feet keyboard shortcuts keypad

Explanation:

Step1: Use cosine function in right - triangle.

Let the length of the ramp be $l$, the horizontal span be $x = 45$ feet and the angle of the ramp with the horizontal be $\theta=18^{\circ}$. In a right - triangle, $\cos\theta=\frac{x}{l}$. So, $l=\frac{x}{\cos\theta}$.

Step2: Substitute the values.

Substitute $x = 45$ and $\theta = 18^{\circ}$ into the formula. We know that $\cos(18^{\circ})\approx0.951057$. Then $l=\frac{45}{\cos(18^{\circ})}=\frac{45}{0.951057}\approx47.3155$.

Answer:

$47.3155$