Question

1. a ramp is placed from a ditch to a main road 2 ft. above the ditch. if the length of the ramp is 12 ft., how far away is the bottom of the ramp from the road?

Explanation:

Step1: Identify as right - triangle problem

We can consider a right - triangle where the height (opposite side) is the height of the road above the ditch ($a = 2$ ft) and the hypotenuse is the length of the ramp ($c = 12$ ft). We want to find the base ($b$).

Step2: Apply Pythagorean theorem

The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$. Rearranging for $b$, we get $b=\sqrt{c^{2}-a^{2}}$.

Step3: Substitute values

Substitute $a = 2$ and $c = 12$ into the formula: $b=\sqrt{12^{2}-2^{2}}=\sqrt{144 - 4}=\sqrt{140}$.

Step4: Simplify

$\sqrt{140}=\sqrt{4\times35}=2\sqrt{35}\approx 2\times5.916\approx11.83$ ft.

Answer:

$2\sqrt{35}\text{ ft}\approx11.83$ ft