Question

Jessica's grandfather needs a wheelchair ramp to access his house. If the angle of elevation of the ramp is 25 degrees and the height from the base of the ramp to the door is 4 feet, what is the length of the ramp? Round your answer to the nearest tenth.

Answer 1

The length of the wheelchair ramp is approximately 9.5 feet when rounded to the nearest tenth by using the sine of the angle of elevation (25 degrees) and the height of the ramp (4 feet).

Step-by-step explanation:

To find the length of the ramp, we can use the relationship between the angle of elevation, the height of the ramp, and the hypotenuse (length of the ramp) given by trigonometric functions. Specifically, the sine of the angle of elevation is equal to the opposite side over the hypotenuse.

We have: sin(25°) = opposite/hypotenuse, where the opposite side is the height of the ramp given as 4 feet. By rearranging this equation and solving for the hypotenuse, we obtain the length of the ramp.

Procedure:

1. Calculate sine of the angle of elevation: sin(25°).
2. Use the sine to find the hypotenuse (ramp length): hypotenuse = opposite / sin(25°).
3. Plug in the given height (opposite side) into the equation and solve for the hypotenuse.

The length of the ramp comes out to:

Length = 4 / sin(25°)

Use a calculator to find sin(25°) and divide 4 by this number.

Let's compute the length:

sin(25°) ≈ 0.4226

Length ≈ 4 / 0.4226 ≈ 9.46 feet

Hence, the length of the ramp is approximately 9.5 feet when rounded to the nearest tenth.