Question

if you place a 24 - foot ladder against the top of a 20 - foot building, how many feet will the bottom of the ladder be from the bottom of the building? round to the nearest tenth of a foot.

Explanation:

Step1: Apply Pythagorean theorem

Let the distance from the bottom of the ladder to the bottom of the building be $x$. The height of the building is $a = 20$ feet and the length of the ladder is $c=24$ feet. According to the Pythagorean theorem $a^{2}+x^{2}=c^{2}$, so $x^{2}=c^{2}-a^{2}$.

Step2: Substitute values

Substitute $a = 20$ and $c = 24$ into the equation $x^{2}=c^{2}-a^{2}$. We get $x^{2}=24^{2}-20^{2}=576 - 400=176$.

Step3: Solve for $x$

Take the square - root of both sides: $x=\sqrt{176}\approx 13.3$.

Answer:

$13.3$