Your town's public library is building a new wheelchair ramp to its entrance. By law, the maximum angle of incline for the ramp is 4.76°. The ramp will have a vertical rise of 1.5 ft. What is the shortest horizontal distance that the ramp can span.
a) 11.5 ft.
b) 2.6 ft.
c) 7.1 ft.
d) 18.0 ft.
I'm not sure which is correct
To determine the shortest horizontal distance that the ramp can span, we can use trigonometry. The trigonometric function that relates the angle of incline, the vertical rise, and the horizontal distance is tangent. The tangent of an angle is equal to the ratio of the opposite side (vertical rise) to the adjacent side (horizontal distance).
Let's calculate the horizontal distance using the tangent function:
tan(angle) = vertical rise / horizontal distance
Plugging in the given values:
tan(4.76°) = 1.5 ft / horizontal distance
To solve for the horizontal distance:
horizontal distance = 1.5 ft / tan(4.76°)
Using a calculator:
horizontal distance ≈ 18.02 ft
The shortest horizontal distance that the ramp can span is approximately 18.02 ft.
Since none of the provided answer choices match exactly, it seems there may be a rounding error. However, the closest option is d) 18.0 ft.
To find the shortest horizontal distance the ramp can span, we need to use trigonometry. We can use the formula:
tan(angle) = opposite/adjacent
In this case, the angle is given as 4.76° and the vertical rise (opposite side) is 1.5 ft. We need to find the adjacent side, which represents the horizontal distance.
Rearranging the formula, we get:
adjacent = opposite / tan(angle)
Plugging in the values:
adjacent = 1.5 ft / tan(4.76°)
Using a scientific or graphing calculator, we can find the value of tan(4.76°) ≈ 0.0836.
So, adjacent = 1.5 ft / 0.0836 ≈ 17.9506 ft.
Therefore, the shortest horizontal distance that the ramp can span is approximately 17.9506 ft.
Among the given options, the closest value to 17.9506 ft is option d) 18.0 ft.