If you place a 35 -foot ladder against the top of a 26 -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.

To find out how far the bottom of the ladder is from the building, you can use the Pythagorean theorem. The ladder acts as the hypotenuse (35 feet), the height of the building is one leg (26 feet), and the distance from the building's base to the bottom of the ladder is the other leg. Using the formula \( a^2 + b^2 = c^2 \): - \( 26^2 + b^2 = 35^2 \) - \( 676 + b^2 = 1225 \) - \( b^2 = 1225 - 676 \) - \( b^2 = 549 \) - \( b = \sqrt{549} \approx 23.4 \) So, the bottom of the ladder will be approximately 23.4 feet from the bottom of the building. --- Did you know that the Pythagorean theorem was named after the ancient Greek mathematician Pythagoras? He was not only a keen number cruncher but also a philosopher! The theorem was known to civilizations like the Babylonians long before Pythagoras, proving that math has been a key player in architecture for ages. Using ladders safely is not just a building site cliché — it’s essential! Ensure the base of your ladder is one foot away from the wall for every four feet of height. This rule keeps you stable while maintaining a lower risk of accidents. Always check for stability, avoid placing ladders on uneven ground, and don’t forget those safety goggles if you're working up high!