Question

20 multiple choice 2 points a ramp 24.3 feet long reaches up to a platform from level ground. if the ramps angle of elevation is 8.3°, find the height of the platform. (give your answer in feet and round to the nearest tenth of a foot.)

Explanation:

Step1: Identify the trigonometric relationship

We can use the sine function. In a right - triangle (where the ramp is the hypotenuse, the height of the platform is the opposite side to the angle of elevation), \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Let \(\theta = 8.3^{\circ}\) and the hypotenuse \(c = 24.3\) feet, and the height \(h\) (opposite side) is what we want to find. So, \(\sin(8.3^{\circ})=\frac{h}{24.3}\).

Step2: Solve for \(h\)

Rearrange the formula to \(h = 24.3\times\sin(8.3^{\circ})\).
We know that \(\sin(8.3^{\circ})\approx0.144\) (using a calculator: \(\sin(8.3^{\circ})=\sin(8^{\circ}18')\approx0.144\)).
Then \(h = 24.3\times0.144\).
\(h=24.3\times0.144 = 3.5\) (rounded to the nearest tenth).

Answer:

\(3.5\) feet