Question

ramp 2 will be located on the side of the front porch. what is the ramp’s length to the nearest tenth of a foot? 1.5 ft. 2.5 ft. x

Explanation:

Step1: Identify the triangle type

This is a right - triangle, so we can use the Pythagorean theorem. The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse, and $a$ and $b$ are the legs of the right - triangle. Here, we know one leg $a = 1.5$ ft and the hypotenuse $c=2.5$ ft, and we want to find the other leg $x$ (let $b = x$). Rearranging the Pythagorean theorem to solve for $b$ (or $x$), we get $b=\sqrt{c^{2}-a^{2}}$.

Step2: Substitute the values into the formula

Substitute $a = 1.5$ and $c = 2.5$ into the formula $x=\sqrt{c^{2}-a^{2}}$. First, calculate $c^{2}$ and $a^{2}$:
$c^{2}=(2.5)^{2}=6.25$
$a^{2}=(1.5)^{2}=2.25$
Then, $c^{2}-a^{2}=6.25 - 2.25=4$

Step3: Calculate the square root

Now, find the square root of $4$: $x=\sqrt{4}=2.0$

Answer:

The length of the ramp is $2.0$ feet.