Step 1: Understand that the ladder, the wall, and the ground form a right triangle.
Step 2: Identify the lengths of the sides of the triangle. The ladder is the hypotenuse (25 meters), the distance from the wall to the foot of the ladder is one side (7 meters), and the height the ladder reaches on the wall is the other side (unknown).
Step 3: Use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). The formula is: c^2 = a^2 + b^2.
Step 4: In our case, let c = 25 meters (the ladder), a = 7 meters (the distance from the wall), and b = the height we want to find.
Step 5: Rearrange the formula to find b: b^2 = c^2 - a^2.
Step 6: Substitute the values into the formula: b^2 = 25^2 - 7^2.
Step 7: Calculate 25^2, which is 625, and 7^2, which is 49.
Step 8: Subtract 49 from 625: 625 - 49 = 576.
Step 9: Take the square root of 576 to find b: √576 = 24.
Step 10: Conclude that the height the ladder reaches on the wall is 24 meters.
