Question

3 multiple choice 1 point a ramp 23.9 feet long reaches up to a platform from level ground. if the ramps angle of elevation is 9.1°, find the height of the platform. (give your answer in feet and round to the nearest tenth of a foot.) 4.3 feet 4.0 feet 3.8 feet 4.1 feet 4.2 feet

Explanation:

Step1: Identify the trigonometric relationship

We have a right - triangle where the length of the ramp is the hypotenuse ($c = 23.9$ feet) and the height of the platform is the side opposite the given angle of elevation ($\theta=9.1^{\circ}$). We use the sine function, $\sin\theta=\frac{opposite}{hypotenuse}$.

Step2: Set up the equation

Let $h$ be the height of the platform. Then $\sin(9.1^{\circ})=\frac{h}{23.9}$.

Step3: Solve for $h$

$h = 23.9\times\sin(9.1^{\circ})$.
We know that $\sin(9.1^{\circ})\approx0.158$.
So $h = 23.9\times0.158=3.7762\approx3.8$ feet.

Answer:

3.8 feet