To find the length of the ramp, we can use the sine function in trigonometry, which relates the angle of elevation and the opposite side (the height of the ramp) to the hypotenuse (the length of the ramp).
The sine function is defined as: \[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]
In this case:
- The opposite side (height of the ramp) is 2 feet.
- The angle \(\theta\) is 20°.
- The hypotenuse is the length of the ramp, which we will call \(L\).
We can rearrange the sine function to solve for \(L\): \[ L = \frac{\text{opposite}}{\sin(\theta)} = \frac{2}{\sin(20°)} \]
Now, we calculate \(\sin(20°)\): Using a calculator, \[ \sin(20°) \approx 0.342 \]
Now we can calculate \(L\): \[ L = \frac{2}{0.342} \approx 5.85 \text{ feet} \]
So, the length of the ramp needs to be approximately 5.85 feet.
The correct response is: 5.85 feet
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