A 10-meter ladder is leaning against a wall. The base of the ladder is 6 meters from the wall. How high up the wall does the ladder reach?

Brief description:

• Ladder length (hypotenuse): 10 m
• Distance from wall (one leg): 6 m
• Height on wall (other leg): ?

Step-by-step solution:

1. Step 1: Identify the components as sides of a right-angled triangle. The ladder is the hypotenuse, the distance from the wall is one leg, and the height on the wall is the other leg.
2. Step 2: Apply the Pythagorean theorem: \( a^2 + b^2 = c^2 \), where 'c' is the hypotenuse and 'a' and 'b' are the legs.
3. Step 3: Substitute the known values: \( 6^2 + b^2 = 10^2 \)
4. Step 4: Calculate the squares: \( 36 + b^2 = 100 \)
5. Step 5: Isolate \( b^2 \): \( b^2 = 100 - 36 \)
6. Step 6: Calculate \( b^2 \): \( b^2 = 64 \)
7. Step 7: Find 'b' by taking the square root of both sides: \( b = \sqrt{64} \)
8. Step 8: Calculate the final height: \( b = 8 \) m.

Answer: 8 m