Question

1. scott is using a 12 - foot ramp to help load furniture into the back of a moving truck. if the back of the truck is 3.5 feet from the ground, what is the horizontal distance from where the ramp touches the ground to the truck?

Explanation:

Step1: Identify the problem type

This is a right triangle problem where the ramp is the hypotenuse, the height of the truck bed is one leg, and we need to find the other leg (horizontal distance). We can use the Pythagorean theorem, \(a^2 + b^2 = c^2\), where \(c\) is the hypotenuse (ramp length), \(a\) is the height (3.5 feet), and \(b\) is the horizontal distance we need to find.

Step2: Plug in the known values

Let \(c = 12\) (ramp length), \(a = 3.5\) (height of truck bed). We need to solve for \(b\). Rearranging the Pythagorean theorem: \(b = \sqrt{c^2 - a^2}\)

Step3: Calculate \(c^2\) and \(a^2\)

\(c^2 = 12^2 = 144\)
\(a^2 = 3.5^2 = 12.25\)

Step4: Subtract and take the square root

\(b = \sqrt{144 - 12.25} = \sqrt{131.75} \approx 11.48\) (rounded to two decimal places)

Answer:

The horizontal distance is approximately \(11.48\) feet.