Use the image to answer the 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
0.68 feet
0.68 feet
5.49 feet
5.49 feet
5.85 feet
5.85 feet
2.13 feet
2.13 feet
5.85 feet
To find the length of the ramp, use the trigonometric function tangent, which is opposite over adjacent. In this case, the opposite side is 2 feet and the angle is 20°.
tan(20°) = opposite/adjacent
tan(20°) = 2/adjacent
adjacent = 2/tan(20°)
adjacent ≈ 5.85 feet
Therefore, the ramp needs to be approximately 5.85 feet long.