Question

page 15 of 15 Solving Right Triangles Quick Check 5 of 55 of 5 Items Question Use the image to answer the 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 5.85 feet Skip to navigation

Answer 1

To find the length of the ramp, we can use the properties of right triangles, specifically the sine function.

In a right triangle:

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

In this case:
- \(\theta = 20^\circ\)
- The height of the ramp (the opposite side) = 2 feet
- The length of the ramp (the hypotenuse) = \(x\)

Using the sine function, we can set up the equation:

\[
\sin(20^\circ) = \frac{2}{x}
\]

To find \(x\), rearranging the equation gives:

\[
x = \frac{2}{\sin(20^\circ)}
\]

Now, calculate \(\sin(20^\circ)\):

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

Now substitute this value into the equation:

\[
x = \frac{2}{0.3420} \approx 5.85 \text{ feet}
\]

Therefore, the length of the ramp has to be approximately **5.85 feet**. The correct response is:

**5.85 feet**.