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 13.2 feet 30.0 feet

Explanation:

Step1: Identify trigonometric ratio

We use cosine: $\cos\theta = \frac{\text{adjacent}}{\text{hypotenuse}}$
Here, $\theta=15^\circ$, adjacent side = 10 ft, hypotenuse = ramp length $L$.

Step2: Rearrange to solve for $L$

$L = \frac{10}{\cos(15^\circ)}$

Step3: Calculate value

$\cos(15^\circ)\approx0.9659$, so $L\approx\frac{10}{0.9659}\approx10.35$

Step4: Round to nearest tenth

$L\approx10.4$

Answer:

10.4 feet