Question

if you place a 34 - foot ladder against the top of a building and the bottom of the ladder is 25 feet from the bottom of the building, how tall is the building? round to the nearest tenth of a foot.

Explanation:

Step1: Identify the right - triangle relationship

The ladder, the building, and the ground form a right - triangle. The length of the ladder is the hypotenuse $c = 34$ feet, and the distance from the bottom of the ladder to the bottom of the building is one leg $a = 25$ feet. We want to find the other leg $b$ (height of the building) using the Pythagorean theorem $a^{2}+b^{2}=c^{2}$.

Step2: Rearrange the Pythagorean theorem

We can rewrite the Pythagorean theorem to solve for $b$: $b=\sqrt{c^{2}-a^{2}}$.

Step3: Substitute the values

Substitute $c = 34$ and $a = 25$ into the formula: $b=\sqrt{34^{2}-25^{2}}=\sqrt{(34 + 25)(34 - 25)}=\sqrt{59\times9}=\sqrt{531}$.

Step4: Calculate the value

$\sqrt{531}\approx23.0$ (rounded to the nearest tenth).

Answer:

$23.0$ feet