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. approximately how long is the ramp? round to the nearest tenth. 10.3 feet 13.2 feet 38.6 feet 10.4 feet

Explanation:

Step1: Identify the trigonometric relationship

We have a right triangle where the adjacent side to the \(15^\circ\) angle is 10 feet (distance from base of building to end of ramp), and the ramp is the hypotenuse (\(c\)) we need to find. We use the cosine function, which is \(\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}\). So \(\cos(15^\circ)=\frac{10}{c}\).

Step2: Solve for \(c\)

Rearrange the formula to \(c = \frac{10}{\cos(15^\circ)}\). We know that \(\cos(15^\circ)\approx0.9659\). Then \(c=\frac{10}{0.9659}\approx10.35\), which rounds to 10.4 feet.

Answer:

10.4 feet