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: Use cosine function

Let the length of the ramp be \(l\). We know that \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, \(\theta = 15^{\circ}\) and the adjacent side (along the ground) is \(10\) feet, and the hypotenuse is the length of the ramp \(l\). So, \(\cos15^{\circ}=\frac{10}{l}\).

Step2: Solve for \(l\)

We can rewrite the equation as \(l=\frac{10}{\cos15^{\circ}}\). Since \(\cos15^{\circ}\approx0.9659\), then \(l=\frac{10}{0.9659}\approx10.35\).

Answer:

10.4 feet