A 12 - ft ladder leans against the side of a house. The bottom of the ladder is 8 ft from the side of the house. How high is the top of the ladder from the ground?

The Pythagorean theorem tells you

... (height of ladder) ² + (distance from house) ² = (length of ladder) ²

... (height of ladder) ² + (8 ft) ² = (12 ft) ²

... height of ladder = √ (12² - 8²) ft

... height of ladder = √80 ft ≈ 8.94 ft