To find the length of the ramp, we 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 length of the hypotenuse.
In this case:
- The height of the ramp (opposite side) is 2 feet.
- The angle of elevation is 20°.
We can express this relationship with the following equation: \[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]
Substituting in the values we have: \[ \sin(20°) = \frac{2}{\text{length of ramp}} \]
Let \( L \) represent the length of the ramp. Rearranging the equation gives: \[ L = \frac{2}{\sin(20°)} \]
Now, we need to calculate \( \sin(20°) \).
Using a calculator: \[ \sin(20°) \approx 0.342 \]
Now plug this value into the equation: \[ L = \frac{2}{0.342} \approx 5.85 \text{ feet} \]
Therefore, the length of the ramp is approximately 5.85 feet.
The correct response is: 5.85 feet.
2 answers