SAT and ACT math terms · SAT Math, ACT Math
Pythagorean theorem
Pythagorean theorem: In a right triangle, the square of the hypotenuse equals the sum of the squares of the legs: a² + b² = c².
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What it means
The theorem lets you find a missing side of a right triangle. Common Pythagorean triples, such as 3-4-5, 5-12-13 and 8-15-17, and their multiples save time.
Special right triangles have fixed ratios: 45-45-90 triangles have sides x, x, x√2, and 30-60-90 triangles have sides x, x√3, 2x.
Example
A ladder 13 feet long leans against a wall with its base 5 feet from the wall. It reaches √(169 − 25) = 12 feet up the wall.
On the exam
Right triangles appear in geometry and trigonometry questions on both tests; the SAT reference sheet includes the theorem and special triangles.