If a ladder's base is a feet from the wall and its length is 4a feet, how high up the wall does it reach?

1. The Pythagorean Theorem gives a squared plus b squared equals (4a) squared, where b is the height on the wall. 2. Expanding the right side gives 16 a squared. 3. So b squared equals 16 a squared minus a squared, that is 15 a squared. 4. Taking the positive square root gives b = a times sqrt(15). 5. Using sqrt(17) would come from adding the squares instead of subtracting them. 6. Simply subtracting the lengths ignores the theorem altogether and would put the top of the ladder at 3a feet. _Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 9 "Trigonometric Identities and Equations", section 9.5 Solving Trigonometric Equations_