Question
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Mason wants to use a sheet of fiberboard 21 inches long to create a skateboard ramp with a height of 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.

Ask by Salinas Dunn. in the United States
Feb 04,2025

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Answer

To find the angle of elevation for the skateboard ramp, you need to know the height at its highest end. Once you provide the height in inches, I can calculate the angle using the sine function.

Solution

It appears that the problem statement is missing the height of the ramp. To determine the angle of elevation, we need both the length of the ramp (which you've provided as 21 inches) and the height at its highest end. **Formula to Use:** The angle of elevation (\(\theta\)) can be found using the sine function in a right triangle: \[ \sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}} = \frac{\text{Height}}{21} \] Once you have the height, you can rearrange the formula to solve for \(\theta\): \[ \theta = \sin^{-1}\left(\frac{\text{Height}}{21}\right) \] **Steps:** 1. **Provide the Height:** Please supply the height of the ramp in inches. 2. **Apply the Formula:** Use the height in the sine formula to find the angle of elevation. 3. **Calculate:** Use a calculator to compute the inverse sine and round the result to the nearest tenth of a degree. **Example:** If, for instance, the height of the ramp is **12 inches**, the calculation would be: \[ \theta = \sin^{-1}\left(\frac{12}{21}\right) \approx \sin^{-1}(0.5714) \approx 34.9^\circ \] Please provide the missing height value so I can help you determine the exact angle of elevation.

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Bonus Knowledge

To find the angle of elevation made by the ramp, you can use the sine function from trigonometry. The sine of an angle is the ratio of the opposite side (height of the ramp) to the hypotenuse (length of the fiberboard). If you're using a height of 12 inches (assuming that's what you meant with "height of inches"), the formula would be: sin(θ) = opposite / hypotenuse = height / length = 12 / 21. Calculating this gives sin(θ) = 0.5714. Now use the inverse sine function: θ = sin⁻¹(0.5714). When you compute that, you get approximately 34.8 degrees. So, the angle of elevation of Mason's ramp is about 34.8 degrees when rounded to the nearest tenth! To make a skateboard ramp successful, it’s essential to ensure that the angle isn’t too steep, as this can lead to skateboarding accidents. The ideal angle for a comfortable ramp is usually around 20 to 30 degrees depending on the user's skill level. Always test out the ramp safely with lower angles first to find the best fit!

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