To find the length of the ramp (hypotenuse), you can use the sine function from trigonometry. The sine of an angle in a right triangle is equal to the opposite side divided by the hypotenuse.
In this case, the height of the ramp is the opposite side (2 feet), and the angle of elevation is 20°.
The formula is:
\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]
So, rearranging the formula to find the hypotenuse (the length of the ramp), we have:
\[ \text{hypotenuse} = \frac{\text{opposite}}{\sin(\theta)} \]
Substituting the known values:
\[ \text{hypotenuse} = \frac{2 \text{ feet}}{\sin(20^\circ)} \]
Now, calculate \(\sin(20^\circ)\):
Using a calculator, \(\sin(20^\circ) \approx 0.3420\).
Now substitute this value back into the equation:
\[ \text{hypotenuse} = \frac{2}{0.3420} \approx 5.85 \text{ feet} \]
Thus, the length of the ramp is approximately 5.85 feet.
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