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

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 building is one of the legs $a = 25$ feet. Let the height of the building be $b$.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$. We can solve for $b$: $b=\sqrt{c^{2}-a^{2}}$.
Substitute $a = 25$ and $c = 34$ into the formula: $b=\sqrt{34^{2}-25^{2}}=\sqrt{(34 + 25)(34 - 25)}=\sqrt{59\times9}=\sqrt{531}$.

Step3: Calculate the value of $b$

$\sqrt{531}\approx23.0$ feet.

Answer:

$23.0$ feet