nevaeh wants to use a sheet of fiberboard 35 inches long to create a skateboard ramp with a height of 10.25…

Explanation:

Step1: Identify the geometric relationship

The ramp forms a right triangle where the fiberboard length is the hypotenuse ($c = 35$) and the height is the opposite side ($a = 10.25$).

Step2: Set up the trigonometric ratio

Use the sine function to relate the angle of elevation $\theta$ to the opposite side and hypotenuse. $$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{10.25}{35}$$

Step3: Solve for the angle

Apply the inverse sine function to find the value of $\theta$. $$\theta = \arcsin\left(\frac{10.25}{35}\right)$$

Step4: Calculate and round the value

Compute the numerical value and round to the nearest tenth. $$\theta \approx \arcsin(0.292857) \approx 17.028^\circ$$

Answer:

17.0°