Question

the ladder to the base of the wall is 21 feet. what is the distance from the base of the wall to the bottom of the ladder? provide an answer accurate to the nearest tenth.

Explanation:

Step1: Apply Pythagorean theorem

Let the length of the ladder be the hypotenuse $c = 31$ ft and the height on the wall be $a = 21$ ft. The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$, and we want to find $b$. So, $b=\sqrt{c^{2}-a^{2}}$.

Step2: Substitute values

Substitute $a = 21$ and $c = 31$ into the formula: $b=\sqrt{31^{2}-21^{2}}=\sqrt{(31 + 21)(31 - 21)}$ (using the difference - of - squares formula $x^{2}-y^{2}=(x + y)(x - y)$). Then $b=\sqrt{(52)\times(10)}=\sqrt{520}$.

Step3: Calculate the value

$\sqrt{520}\approx22.8$ (rounded to the nearest tenth).

Answer:

$22.8$ ft