Question

name: date: find an unknown side length in a right triangle kevin is a carpenter and enjoys building things for his neighbors. one of his neighbors uses a wheelchair to get around. kevin wants to help his neighbor move around the outside of his home more easily by building a few wheelchair ramps around his house. the neighbor’s home is elevated, and it has a long front porch and a porch to get to the backyard. kevin decides to build three ramps: two for the front porch and one for the back porch. determine the missing side length of each of kevin’s ramps. ramp 1 will be located at the center of the front porch. what is the slant height of the ramp to the nearest tenth of a foot? 1.5 ft. x 4.8 ft.

Explanation:

Step1: Identify the formula

We use the Pythagorean theorem for a right triangle, which is \(a^2 + b^2 = c^2\), where \(a\) and \(b\) are the legs, and \(c\) is the hypotenuse (slant height \(x\) here).
Let \(a = 1.5\) ft and \(b = 4.8\) ft.

Step2: Substitute the values

Substitute \(a = 1.5\) and \(b = 4.8\) into the formula:
\(x^2 = (1.5)^2 + (4.8)^2\)

Step3: Calculate the squares

Calculate \((1.5)^2 = 2.25\) and \((4.8)^2 = 23.04\).

Step4: Sum the squares

Add the results: \(2.25 + 23.04 = 25.29\).

Step5: Take the square root

Take the square root of \(25.29\) to find \(x\): \(x = \sqrt{25.29} \approx 5.0\) (rounded to the nearest tenth).

Answer:

The slant height of the ramp is approximately \(\boldsymbol{5.0}\) feet.