Question

if you place a 38 - foot ladder against the top of a 25 - 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: Identify the problem as a right - triangle problem

The ladder, the building, and the ground form a right - triangle. The length of the ladder is the hypotenuse $c = 38$ feet and the height of the building is one of the legs $a = 25$ feet. We want to find the other leg $b$. According to the Pythagorean theorem $a^{2}+b^{2}=c^{2}$.

Step2: Rearrange the Pythagorean theorem to solve for $b$

We get $b=\sqrt{c^{2}-a^{2}}$. Substitute $c = 38$ and $a = 25$ into the formula: $b=\sqrt{38^{2}-25^{2}}=\sqrt{(38 + 25)(38 - 25)}=\sqrt{63\times13}=\sqrt{819}$.

Step3: Calculate the value of $b$

$\sqrt{819}\approx28.6$ feet.

Answer:

$28.6$ feet