Question

question 7 of 16, step 1 of 1 the ramp of a moving truck touches the ground 10 feet away from the end of the truck. if the ramp makes an angle of 25° relative to the ground, what is the length of the ramp? round your answer to two decimal places. answer feet

Explanation:

Step1: Identify the trigonometric relation

We know the adjacent - side to the angle and want to find the hypotenuse. Use cosine function $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, $\theta = 25^{\circ}$ and the adjacent side $x = 10$ feet, and let the length of the ramp (hypotenuse) be $l$. So, $\cos(25^{\circ})=\frac{10}{l}$.

Step2: Solve for $l$

We can re - arrange the formula to $l=\frac{10}{\cos(25^{\circ})}$. Since $\cos(25^{\circ})\approx0.9063$, then $l=\frac{10}{0.9063}\approx11.03$.

Answer:

$11.03$