Question

Tyrese is building a ramp up to his home. He knows the height of the ramp is 2 feet. If the angle of elevation of the ramp is 20°, how long does the ramp have to be?

(1 point)
Responses

5.49 feet
5.49 feet

5.85 feet
5.85 feet

2.13 feet
2.13 feet

0.68 feet
0.68 feet

Answer 1

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**.