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 degrees, how long does the ramp have to be?

0.68 feet
5.49 feet
2.13 feet
5.85 feet

Answer 1

To find the length of the ramp, we can use the sine function from trigonometry, which relates the angle of elevation to the height and length of the hypotenuse (in this case, the length of the ramp).

The sine of the angle of elevation (θ) is given by the formula:

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

In this scenario:
- \(θ = 20^\circ\) (the angle of elevation)
- Opposite side = height of the ramp = 2 feet
- Hypotenuse = length of the ramp (which we need to find)

So we can rewrite the formula as:

\[
\sin(20^\circ) = \frac{2}{\text{length of the ramp}}
\]

Now let's rearrange the formula to solve for the length of the ramp:

\[
\text{length of the ramp} = \frac{2}{\sin(20^\circ)}
\]

Next, we need to calculate \( \sin(20^\circ) \). Using a calculator, we find:

\[
\sin(20^\circ) \approx 0.3420
\]

Now substitute this value back into our equation:

\[
\text{length of the ramp} = \frac{2}{0.3420} \approx 5.85 \text{ feet}
\]

Thus, the length of the ramp is approximately **5.85 feet**.

The answer is **5.85 feet**.