Question

a ramp 40 ft long rises to a platform. the bottom of the platform is 17 ft from the foot of the ramp. find x, the angle of elevation. round your answer to the nearest tenth of a degree.

Explanation:

Step1: Identify the cosine relationship

We know that in a right - triangle, $\cos(x)=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, the adjacent side to the angle $x$ is 17 ft and the hypotenuse is 40 ft. So, $\cos(x)=\frac{17}{40}$.

Step2: Solve for the angle $x$

We use the inverse - cosine function. $x = \cos^{-1}(\frac{17}{40})$.
Calculating $\cos^{-1}(\frac{17}{40})\approx64.0^{\circ}$.

Answer:

$64.0$