Question

Payton is building a ramp up to her home. She knows the height of the ramp is 2.5 feet. If the angle of elevation of the ramp is 22°
22
°
, how long does the ramp have to be?(1 point)
Responses

8.33 feet
8.33 feet

1.01 feet
1.01 feet

2.70 feet
2.70 feet

6.67 feet

Answer 1

To find the length of the ramp, we can use the sine function, which relates the angle of elevation to the opposite side (height of the ramp) and the hypotenuse (length of the ramp).

The sine of an angle is given by the formula:

\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}
\]

In this case:
- \(\theta = 22°\)
- The height of the ramp (opposite side) = 2.5 feet
- Let the length of the ramp (hypotenuse) be \(L\).

Thus, we have:

\[
\sin(22°) = \frac{2.5}{L}
\]

To find \(L\), we rearrange the formula:

\[
L = \frac{2.5}{\sin(22°)}
\]

Now, we can calculate the value of \(L\):

1. First, calculate \(\sin(22°)\). Using a calculator:
\(\sin(22°) \approx 0.3746\).

2. Then, substitute this value into the equation:

\[
L \approx \frac{2.5}{0.3746} \approx 6.67 \text{ feet}
\]

Therefore, the length of the ramp needs to be approximately **6.67 feet**.