Question

if a skateboard ramp is 7 feet long and has an angle of inclination of 2 degrees, what is the vertical rise of the ramp to the nearest tenth?
2.1 feet
7.0 feet
1.2 feet
0.2 feet

Explanation:

Step1: Use the sine function

In a right - triangle (where the ramp is the hypotenuse), if the length of the hypotenuse \(c = 7\) feet and the angle of inclination \(\theta=2^{\circ}\), and the vertical rise is \(y\). The formula for the sine of an angle in a right - triangle is \(\sin\theta=\frac{y}{c}\).
So, \(y = c\times\sin\theta\).

Step2: Substitute the values

Substitute \(c = 7\) and \(\theta = 2^{\circ}\) into the formula. We know that \(\sin(2^{\circ})\approx0.0349\) (using a calculator in degree mode).
Then \(y=7\times\sin(2^{\circ})\).
\(y = 7\times0.0349\).
\(y=0.2443\approx0.2\) (rounded to the nearest tenth).

Answer:

0.2 feet