Question

a ramp leading into a building makes a 15° angle with the ground. the end of the ramp is 10 feet from the base of the building (along the ground). approximately how long is the ramp? round to the nearest tenth. 10.3 feet 10.4 feet 12.2 feet 38.6 feet

Explanation:

Step1: Define cosine ratio

Let the length of the ramp be $l$. We know $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here $\theta = 15^{\circ}$ and adjacent side to the angle is 10 feet, so $\cos15^{\circ}=\frac{10}{l}$.

Step2: Solve for $l$

$l=\frac{10}{\cos15^{\circ}}$. Since $\cos15^{\circ}\approx0.9659$, then $l=\frac{10}{0.9659}\approx10.4$ feet.

Answer:

10.4 feet