To find the length of the ramp, you can use the sine function from trigonometry. The sine of an angle in a right triangle is defined as the ratio of the length of the opposite side to the hypotenuse.
In this case:
- The height of the ramp (opposite side) is 2 feet.
- The angle of elevation is 20°.
Using the sine function:
\[ \sin(20°) = \frac{\text{height}}{\text{length of the ramp}} \]
We can rearrange this to find the length of the ramp:
\[ \text{length of the ramp} = \frac{\text{height}}{\sin(20°)} \]
Now, plug in the height:
\[ \text{length of the ramp} = \frac{2}{\sin(20°)} \]
Using a calculator to find \(\sin(20°)\):
\[ \sin(20°) \approx 0.3420 \]
Now substitute this value into the equation:
\[ \text{length of the ramp} = \frac{2}{0.3420} \approx 5.85 \text{ feet} \]
Thus, the length of the ramp has to be approximately 5.85 feet.