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Question

A triangle. The hypotenuse descends from left to right and is labeled, Ramp up to the house. The bottom right angle is labeled 20 degrees. The vertical leg of the triangle is labeled 2 feet.

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

5.85 feet
5.85 feet

5.49 feet
5.49 feet

0.68 feet
0.68 feet

2.13 feet
2.13 feet

Answer 1

To find the length of the ramp (the hypotenuse of the triangle), we can use trigonometric functions.

Using the sine function:

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

In this case, the opposite side is the height of the ramp (2 feet), and the angle \(\theta\) is 20 degrees. We need to find the hypotenuse (ramp length).

Rearranging the sine function gives us:

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

Substituting the known values:

\[ \text{hypotenuse} = \frac{2 , \text{feet}}{\sin(20^\circ)} \]

Using a calculator, we find:

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

Now calculate the hypotenuse:

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

Therefore, the length of the ramp Tyrese needs is approximately 5.85 feet.

So the correct response is:

5.85 feet.