Question

multiple choice 1 point
rajani wants to use a sheet of fiberboard 31 inches long to create a skateboard ramp with a 19° angle of elevation from the ground. how high will the ramp rise from the ground at its highest end? round your answer to the nearest tenth of an inch.
10.7 in.
9.8 in.
10.1 in.
29.3 in.

Explanation:

Step1: Identify the trigonometric relationship

We know that in a right - triangle (the ramp forms a right - triangle with the ground), the sine function is defined as \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, the hypotenuse (length of the fiberboard) \(c = 31\) inches, the angle of elevation \(\theta=19^{\circ}\), and the height \(h\) (opposite side to the angle \(\theta\)) is what we want to find. So, \(\sin\theta=\frac{h}{c}\).

Step2: Solve for \(h\)

Substitute \(\theta = 19^{\circ}\) and \(c = 31\) into the formula \(h = c\times\sin\theta\).
Since \(\sin(19^{\circ})\approx0.3256\), then \(h=31\times\sin(19^{\circ})\).
\(h = 31\times0.3256=10.0936\approx10.1\)

Answer:

10.1 in.