38. For maximum accessibility, a wheelchair ramp should have a slope

between 1/16 and 1/20. What is the range of angle measures that a ramp should make
with a horizontal line? Round to the nearest degree.

1/16=tan-11/16=9.09°

Similarly:
1/20=tan-11/20=?

645

To find the range of angle measures that a wheelchair ramp should make with a horizontal line, we can use the tangent trigonometric function.

The tangent of an angle is calculated by dividing the opposite side of a right triangle by the adjacent side. In this case, the opposite side is the height of the ramp, and the adjacent side is the length of the ramp.

Let's first calculate the slope of the ramp based on the given range. The slope of a ramp is calculated by dividing the rise (height) of the ramp by the run (length) of the ramp.

1. Slope for 1/16 range:
slope = rise / run
slope = 1 / 16
slope = 0.0625

2. Slope for 1/20 range:
slope = rise / run
slope = 1 / 20
slope = 0.05

Now, we can calculate the angle range using the inverse tangent function (arctan).

1. Maximum angle for 1/16 range:
angle = arctan(slope)
angle = arctan(0.0625)
angle ≈ 3.578 degrees

2. Maximum angle for 1/20 range:
angle = arctan(slope)
angle = arctan(0.05)
angle ≈ 2.862 degrees

Therefore, the range of angle measures that a wheelchair ramp should make with a horizontal line, rounded to the nearest degree, is approximately 3 to 4 degrees.

To find the range of angle measures that a wheelchair ramp should make with a horizontal line, we can use trigonometry. The tangent function can help us find the angle given the slope.

The slope of a ramp is defined as the rise (vertical change) divided by the run (horizontal change). In this case, the slope should be between 1/16 and 1/20.

Let's use the example slope of 1/16 to demonstrate the calculation. We can find the angle by taking the inverse tangent (arctan) of the slope.

angle = arctan(slope)

angle = arctan(1/16)

Using a scientific calculator or an online calculator, we can find that the arctan(1/16) is approximately 3.58 degrees.

So, for the slope of 1/16, the angle that the ramp should make with a horizontal line is approximately 3.58 degrees.

Now, let's repeat the calculation with the slope of 1/20.

angle = arctan(1/20)

Using the same procedure, we find that the arctan(1/20) is approximately 2.86 degrees.

So, for the slope of 1/20, the angle that the ramp should make with a horizontal line is approximately 2.86 degrees.

Therefore, the range of angle measures for the wheelchair ramp slope is approximately 2.86 degrees to 3.58 degrees, rounded to the nearest degree.