\( \square \begin{array}{l}\text { A ladder that is } 13 \text { feet long leans against a building. The bottom of the ladder is } 5 \text { feet away from the base } \\ \text { of the building. How far up the side of the bulding does the ladder reach? } \\ \text { feet }\end{array} \) freck answea

To find out how far up the side of the building the ladder reaches, you can use the Pythagorean theorem. The ladder, the distance from the base of the building to the bottom of the ladder, and the distance up the wall form a right triangle. Here, the length of the ladder is the hypotenuse (13 feet), the distance from the wall (5 feet) is one leg, and the height up the wall is the other leg. Using the formula \( a^2 + b^2 = c^2 \), where \( c = 13 \) feet and \( b = 5 \) feet, you can calculate the height \( a \): \[ a^2 + 5^2 = 13^2 \] \[ a^2 + 25 = 169 \] \[ a^2 = 144 \] \[ a = 12 \] Thus, the ladder reaches **12 feet** up the side of the building! If you ever find yourself with a ladder and a wall, don’t forget to measure first! A common mistake is not to check that the ladder is stable and at the right angle before climbing. Always make sure that you’re using the ladder safely, adhering to all safety guidelines. Happy climbing!