ACT Preparation / Unit 13 ACT 1224 worked example, 60 to 90 seconds
Using the Pythagorean Theorem
The idea
The Pythagorean theorem is applied in three steps. First, find or sketch the right triangle and identify the hypotenuse, the side opposite the right angle. Second, substitute the known sides: c² = a² + b² for a missing hypotenuse, or a² = c² − b² for a missing leg. Third, take the square root and simplify, after checking whether the sides form a known triple.
In practice
Worked example: a 13-foot ladder leans against a wall with its foot 5 feet from the wall. How high does it reach? The ladder is the hypotenuse: h² = 13² − 5² = 169 − 25 = 144, so h = 12 feet, the 5, 12, 13 triple. Second: is a triangle with sides 7, 9 and 12 right? 49 + 81 = 130, not 144, so it is not.
Where people slip
For a missing leg, subtract. Adding 13² and 5² treats the ladder as a leg and gives √194, about 13.9 feet, longer than the ladder itself.
Your place on the trail
Every lesson rests on earlier ones and opens later ones. Tap any to jump.
Something wrong in this lesson? Flag it · Sources for ACT Preparation