To find the angle of elevation of the ramp, we can use trigonometry. Specifically, we will use the sine function, since we know the opposite side (the height of the ramp) and the hypotenuse (the length of the ramp).
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Identify the sides:
- The height (opposite side) from the ground to the doorway is 1 foot.
- The length of the ramp (hypotenuse) is 5 feet.
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Use the sine function: The sine of an angle in a right triangle is defined as:
\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]
Here, \(\theta\) is the angle of elevation we want to find.
Plugging in the values:
\[ \sin(\theta) = \frac{1}{5} \]
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Calculate \(\theta\): To find \(\theta\), we need to take the inverse sine (arcsin) of \(\frac{1}{5}\):
\[ \theta = \arcsin\left(\frac{1}{5}\right) \]
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Compute the angle (using a calculator):
\[ \theta \approx \arcsin(0.2) \approx 11.54^\circ \]
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Round to the nearest degree: The angle of elevation of the ramp to the nearest degree is approximately:
\[ \theta \approx 12^\circ \]
Thus, the angle of elevation of the ramp is 12 degrees.