Question

a. a wheelchair ramp with a length of 137 inches has a horizontal distance of 105 inches. what is the ramps vertical distance?
b. construction laws are very specific when it comes to access ramps for the disabled. every vertical rise of 1 inch requires a horizontal run of 12 inches. does this ramp satisfy the requirements?

Explanation:

Step1: Apply Pythagorean theorem

Let the vertical distance be $x$. According to the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c = 137$ (hypotenuse) and $b = 105$ (horizontal side), so $x^{2}+105^{2}=137^{2}$.

Step2: Solve for $x$

First, calculate $137^{2}=18769$ and $105^{2}=11025$. Then $x^{2}=18769 - 11025=7744$. Taking the square - root of both sides, $x=\sqrt{7744}=88$ inches.

Step3: Check ramp requirements

The ratio of vertical rise to horizontal run for the ramp is $\frac{88}{105}\approx0.838$. The required ratio is $\frac{1}{12}\approx0.083$. Since $\frac{88}{105}>\frac{1}{12}$, the ramp does not satisfy the requirements.

Answer:

a. 88 inches
b. No