Question

a ramp 15 ft long rises to a platform that is 12 ft off the ground. find x, the angle of elevation of the ramp. round your answer to the nearest tenth of a degree.

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, \(\sin x=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, the opposite side to angle \(x\) is \(12\) (height of the platform) and the hypotenuse is \(15\) (length of the ramp). So, \(\sin x=\frac{12}{15}\).

Step2: Simplify the ratio and find the angle

Simplify \(\frac{12}{15}=\frac{4}{5} = 0.8\). Then, \(x=\sin^{- 1}(0.8)\). Using a calculator, \(x\approx53.1^{\circ}\).

Answer:

\(53.1\)