Final answer:
The ladder touches the wall of the house at a height of 8 feet above the ground.
Step-by-step explanation:
The ladder forms a right triangle with the wall and the ground. We can use the Pythagorean theorem to find the height of the ladder. The base of the ladder is 6 feet and the ladder itself is 10 feet long, so the height of the ladder can be calculated as follows:
Height of ladder = square root of (length of ladder squared - base of ladder squared)
Height of ladder = square root of (10 squared - 6 squared)
Height of ladder = square root of (100 - 36)
Height of ladder = square root of 64
Height of ladder = 8 feet
Therefore, the ladder touches the wall of the house at a height of 8 feet above the ground.