To meet the requirements of the Americans with Disabilities...

To meet the requirements of the Americans with Disabilities Act (ADA) a wheelchair ramp must have a slope of $1: 12$ or less. That is, for every $1 \mathrm{in}$. of "rise," there must be at least $12 \mathrm{in}$. of "run." (See Example 9) a. If a wheelchair ramp is constructed with the maximum slope, what angle does the ramp make with the ground? Round to the nearest tenth of a degree. b. If the ramp is $22 \mathrm{ft}$ long, how much elevation does the ramp provide? Round to the nearest tenth of a foot.

To meet the requirements of the Americans with Disabilities Act (ADA) a wheelchair ramp must have a slope of $1: 12$ or less. That is, for every $1 \mathrm{in}$. of "rise," there must be at least $12 \mathrm{in}$. of "run." (See Example 9)
a. If a wheelchair ramp is constructed with the maximum slope, what angle does the ramp make with the ground? Round to the nearest tenth of a degree.
b. If the ramp is $22 \mathrm{ft}$ long, how much elevation does the ramp provide? Round to the nearest tenth of a foot.

Key Concepts

Slope as a Ratio

The concept of slope as a ratio defines the relationship between the vertical rise and the horizontal run of an inclined plane. In many applications, such as ramp design, a particular maximum slope is specified, meaning that for every unit of vertical distance, a proportional number of units is required in horizontal distance. This ratio helps in determining the steepness of the ramp and ensuring it meets certain guidelines or standards.

Trigonometric Functions – Tangent and Inverse Tangent

In right triangle geometry, the tangent of an angle is defined as the ratio of the opposite side (vertical rise) to the adjacent side (horizontal run). Using the inverse tangent (arctan) allows one to calculate the angle of inclination when the ratio of rise to run is known. This is a crucial step in determining how steep an inclined surface is, particularly when working with maximum permissible slopes.

Right Triangle Relationships – Sine Function for Vertical Rise

Once the angle of inclination is known or the hypotenuse (length of the ramp) is given, the sine function can be used to determine the vertical rise. The sine of the angle in a right triangle is the ratio of the opposite side (vertical height) to the hypotenuse (the ramp’s length). This relationship is useful in calculating the actual elevation achieved by a ramp when its length and angle of incline are specified.

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