This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Identify the known values and the unknown. The ladder, the wall, and the ground form a right-angled triangle. The length of the ladder is the hypotenuse, c = 13 m. The height the ladder reaches on the wall is one leg, a = 12 m. The distance of the ladder's foot from the house is the other leg, b, which we need to find. Step 2: Apply the Pythagorean theorem. The Pythagorean theorem states that a^2 + b^2 = c^2. Substitute the given values into the formula: 12^2 + b^2 = 13^2 Step 3: Solve for b. 144 + b^2 = 169 Subtract 144 from both sides: b^2 = 169 - 144 b^2 = 25 Take the square root of both sides: b = sqrt(25) b = 5 m The ladder is 5 m away from the foot of the house. 3 done, 2 left today. You're making progress.