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)Responses2.13 feet2.13 feet5.49 feet5.49 feet0.68 feet0.68 feet5.85 feet5.85 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 to the hypotenuse. In this problem:

- The height of the ramp (opposite side) is 2 feet.
- The angle of elevation is 20°.
- The length of the ramp (hypotenuse) is what we are trying to find.

Using the sine function:

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

Substituting in our values:

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

To find the length, we can rearrange the equation:

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

Now, calculating \( \sin(20°) \):

\[
\sin(20°) \approx 0.342
\]

Now substitute that value into the equation:

\[
\text{length} = \frac{2}{0.342} \approx 5.85 \text{ feet}
\]

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