Question

tamika wants to use a sheet of fiberboard 27 inches long to create a skateboard ramp with a height of 12.75 inches at its highest end. find the angle of elevation made by the ramp with the ground. round your answer to the nearest tenth of a degree. answer attempt 1 out of 2

Explanation:

Step1: Identify the trigonometric relationship

The ramp forms a right - triangle where the length of the fiberboard is the hypotenuse ($c = 27$ inches) and the height of the ramp is the opposite side ($a=12.75$ inches) with respect to the angle of elevation $\theta$. We use the sine function $\sin\theta=\frac{a}{c}$.

Step2: Calculate the sine of the angle

Substitute $a = 12.75$ and $c = 27$ into the sine formula: $\sin\theta=\frac{12.75}{27}\approx0.4722$.

Step3: Find the angle

To find $\theta$, we take the inverse - sine of 0.4722. So, $\theta=\sin^{- 1}(0.4722)$. Using a calculator, $\theta\approx28.2^{\circ}$.

Answer:

$28.2^{\circ}$