Question

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 reaches the ground to the truck?round to the nearest hundredth.

answer attempt 1 out of 6
additional solution no solution
11.3 ft

Explanation:

Step1: Identify right triangle sides

The ramp is the hypotenuse ($c=12$ ft), truck height is one leg ($a=3.5$ ft). We need the other leg $b$ (horizontal distance). Use Pythagorean theorem: $c^2 = a^2 + b^2$.

Step2: Rearrange to solve for $b$

Rearrange formula to isolate $b$: $b = \sqrt{c^2 - a^2}$

Step3: Substitute values and calculate

Substitute $c=12$, $a=3.5$:

$$\begin{align*} b&=\sqrt{12^2 - 3.5^2}\\ &=\sqrt{144 - 12.25}\\ &=\sqrt{131.75}\\ &\approx11.48 \end{align*}$$

Answer:

11.48 ft