Pregunta
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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 Osborne Stephens. in the United States
Feb 04,2025

Solución de tutoría real

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

Solución

It appears that the height of the skateboard ramp is missing from the problem statement. To determine the angle of elevation (\(\theta\)) that the ramp makes with the ground, we need two key measurements: 1. **Length of the ramp (hypotenuse)**: 21 inches 2. **Height of the ramp (opposite side)**: *[Missing]* The relationship between the angle of elevation, the opposite side (height), and the hypotenuse (ramp length) can be described using the sine function in trigonometry: \[ \sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}} = \frac{\text{Height}}{21} \] To find the angle \(\theta\), you would use the inverse sine (arcsin) function: \[ \theta = \arcsin\left(\frac{\text{Height}}{21}\right) \] **Action Required:** Please provide the height of the skateboard ramp in inches so that I can help you calculate the angle of elevation accurately.

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Bonus Knowledge

To find the angle of elevation of the ramp, we can use trigonometry. The height of the ramp is the opposite side, and the length of the fiberboard is the hypotenuse. If we let \( h \) be the height of the ramp, we can use the sine function: \[ \sin(\theta) = \frac{h}{\text{hypotenuse}} = \frac{h}{21} \] Rearranging gives: \[ \theta = \arcsin\left(\frac{h}{21}\right) \] There's one crucial thing to remember: unless you know the height \( h \), you can’t find the exact angle! So, once you have that height, plug it into the formula and calculate \( \theta \) using a calculator for the arcsin function, rounding to the nearest tenth of a degree. If you have a specific height in mind, let me know, and we can calculate the exact angle together!

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