Question

a ramp is to be built beside the steps to the campus library. find the angle of elevation of the 23 - foot ramp, to the nearest tenth of a degree, if its final height is 4 feet. the ramp makes an angle of approximately ° with the ground. (simplify your answer. round to the nearest tenth as needed.)

Explanation:

Step1: Identify the trigonometric relationship

We have a right - triangle where the hypotenuse is the length of the ramp ($c = 23$ feet) and the opposite side to the angle of elevation $\theta$ is the height of the ramp ($a = 4$ feet). We use the sine function $\sin\theta=\frac{a}{c}$.

Step2: Calculate the sine of the angle

Substitute $a = 4$ and $c = 23$ into the sine formula: $\sin\theta=\frac{4}{23}\approx0.1739$.

Step3: Find the angle

To find $\theta$, we take the inverse - sine of 0.1739. So, $\theta=\sin^{- 1}(0.1739)$. Using a calculator, $\theta\approx10.0^{\circ}$.

Answer:

$10.0$