Question

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

Explanation:

Step1: Identify right triangle sides

Ramp = hypotenuse ($c=12$ ft), height = opposite side ($a=3.5$ ft), horizontal distance = adjacent side ($b$). Use Pythagorean theorem: $a^2 + b^2 = c^2$.

Step2: Rearrange for $b$

$b = \sqrt{c^2 - a^2}$

Step3: Calculate values

$c^2 = 12^2 = 144$, $a^2 = 3.5^2 = 12.25$. So $c^2 - a^2 = 144 - 12.25 = 131.75$.

Step4: Compute square root

$b = \sqrt{131.75} \approx 11.48$

Answer:

Approximately 11.5 feet (or 11.48 feet for more precision)