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 0.68 feet 0.68 feet 2.13 feet 2.13 feet 5.49 feet 5.49 feet 5.85 feet

Answer 1

To find the length of the ramp, you 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 hypotenuse.

In this case:
- The height of the ramp (opposite side) is 2 feet.
- The angle of elevation is 20°.

Using the sine function:

\[
\sin(20°) = \frac{\text{height}}{\text{length of the ramp}}
\]

We can rearrange this to find the length of the ramp:

\[
\text{length of the ramp} = \frac{\text{height}}{\sin(20°)}
\]

Now, plug in the height:

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

Using a calculator to find \(\sin(20°)\):

\[
\sin(20°) \approx 0.3420
\]

Now substitute this value into the equation:

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

Thus, the length of the ramp has to be approximately **5.85 feet**.