Question

a wheelchair ramp with a length of 123 inches has a horizontal distance of 120 inches. what is the ramps vertical distance? the vertical distance of the ramp is

Explanation:

Step1: Apply Pythagorean theorem

Let the vertical distance be \(y\), horizontal distance \(x = 120\) inches and length of the ramp \(c=123\) inches. According to the Pythagorean theorem \(x^{2}+y^{2}=c^{2}\), so \(y^{2}=c^{2}-x^{2}\).

Step2: Substitute values

Substitute \(x = 120\) and \(c = 123\) into the formula: \(y^{2}=123^{2}-120^{2}=(123 + 120)(123-120)\) (using \(a^{2}-b^{2}=(a + b)(a - b)\)). Then \(y^{2}=(243)\times(3)=729\).

Step3: Solve for \(y\)

Take the square root of both sides: \(y=\sqrt{729}=27\) inches.

Answer:

27 inches