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 38.6 feet

Explanation:

Step1: Identify trigonometric ratio

We have a right triangle where the adjacent side to the $15^\circ$ angle is 10 feet, and the ramp is the hypotenuse. Use cosine: $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$

Step2: Rearrange to solve for hypotenuse

Let $L$ = length of ramp. Rearrange formula: $L = \frac{\text{adjacent}}{\cos(\theta)}$
Substitute values: $L = \frac{10}{\cos(15^\circ)}$

Step3: Calculate the value

$\cos(15^\circ) \approx 0.9659$, so $L \approx \frac{10}{0.9659} \approx 10.35$

Step4: Round to nearest tenth

Round 10.35 to 10.4

Answer:

10.4 feet