A25 foot ladder leans against a wall 7 feet from the base of the wall. how high does the ladder touch?

Use Pythagorean theorem to figure this out:

a² + b² = c²     In this case since you are trying to find the A leg, the formula would be: c² - b² = a²

25² = 625      7² = 49      625 - 49 = 576     √576 = 24    

How high does the ladder touch? 24 ft.

A² + b² = c²

a² + 7² = 25²

a² = 25² - 7²

a² = 576

a = 24

The height is 24 feet.