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 (10 meters), the distance from the wall to the foot of the ladder is one side (6 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: Substitute the known values into the formula: 10^2 = 6^2 + height^2.
Step 5: Calculate 10^2, which is 100, and 6^2, which is 36. So, the equation becomes: 100 = 36 + height^2.
Step 6: Rearrange the equation to find height^2: height^2 = 100 - 36.
Step 7: Calculate 100 - 36, which equals 64. So, height^2 = 64.
Step 8: Take the square root of 64 to find the height: height = √64.
Step 9: Calculate the square root of 64, which is 8. Therefore, the height the ladder reaches on the wall is 8 meters.
