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.

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

2.13 feet
2.13 feet

5.49 feet
5.49 feet

5.85 feet
5.85 feet

0.68 feet

Answer 1

To find the length of the ramp (hypotenuse of the triangle), we can use the sine function in trigonometry. The sine of an angle in a right triangle is defined as the opposite side (height) over the hypotenuse (ramp length).

Given:

• Height (opposite side) = 2 feet
• Angle of elevation = 20°

Using the sine function: \[ \sin(20^\circ) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{2}{\text{hypotenuse}} \]

To find the hypotenuse (length of the ramp), we can rearrange the formula: \[ \text{hypotenuse} = \frac{2}{\sin(20^\circ)} \]

Now we need to calculate \(\sin(20^\circ)\): \(\sin(20^\circ) \approx 0.3420\)

Substituting this value into our equation: \[ \text{hypotenuse} = \frac{2}{0.3420} \approx 5.85 \text{ feet} \]

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

The correct answer is: 5.85 feet