Question

jacklyn is building a cat - house for her cats. she designs a ramp from one level to the other for them to climb. the ramp length is 4 feet, and the difference between the two levels is 2.5 feet. using the inverse sine function, what is the approximate angle of elevation formed by the ramp? round your answer to the nearest whole degree. (1 point)

Explanation:

Step1: Identify sine - function components

The ramp forms a right - triangle. The length of the ramp is the hypotenuse $c = 4$ feet and the vertical distance (opposite side to the angle of elevation $\theta$) is $a=2.5$ feet. The sine of an angle in a right - triangle is defined as $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$.

Step2: Calculate $\sin\theta$

$\sin\theta=\frac{2.5}{4}= 0.625$.

Step3: Find the angle using inverse sine

$\theta=\sin^{- 1}(0.625)$. Using a calculator, $\sin^{-1}(0.625)\approx38.68^{\circ}$. Rounding to the nearest whole degree, $\theta\approx39^{\circ}$.

Answer:

$39$