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° , how long does the ramp have to be?(1 point) Responses 8.33 feet 8.33 feet 6.67 feet 6.67 feet 1.01 feet 1.01 feet 2.70 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 opposite side (height of the ramp) to the hypotenuse (length of the ramp).

Here, the height of the ramp (opposite side) is 2.5 feet, and the angle of elevation is 22°.

The formula we can use is:

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

In this case, we want to solve for the hypotenuse (length of the ramp), so we rearrange the formula:

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

Substituting the known values:

\[
\text{hypotenuse} = \frac{2.5}{\sin(22°)}
\]

Calculating \(\sin(22°)\):

\[
\sin(22°) \approx 0.3746
\]

Now plug this value back into the equation:

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

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