Question

a 25 foot ladder is leaning against the side of a building. how far up the side of the building does the ladder reach? 25 ft 7 ft 12

Explanation:

Step1: Recognize right - triangle

The ladder, the building, and the ground form a right - triangle. The length of the ladder is the hypotenuse $c = 25$ ft and the distance from the base of the ladder to the building is one leg $a = 7$ ft. We want to find the other leg $b$ (height on the building).

Step2: Apply Pythagorean theorem

The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$. Rearranging for $b$, we get $b=\sqrt{c^{2}-a^{2}}$. Substitute $a = 7$ and $c = 25$ into the formula: $b=\sqrt{25^{2}-7^{2}}=\sqrt{(25 + 7)(25 - 7)}=\sqrt{32\times18}=\sqrt{576}$.

Step3: Calculate the value of $b$

$\sqrt{576}=24$ ft.

Answer:

24 ft