Apply the Pythagorean theorem and basic trigonometric ratios to solve for unknown side lengths.
58 original right triangles and trigonometry questions in the SAT Ranker bank, with instant scoring and an Elo-based rank once you sign up. Below are a few free samples with full explanations.
A right triangle has legs of length 24 and 45. What is the length of the hypotenuse?
By the Pythagorean theorem: 24² + 45² = 576 + 2025 = 2601, so the hypotenuse is √2601 = 51.
A right triangle has legs of length 21 and 72. What is the length of the hypotenuse?
By the Pythagorean theorem: 21² + 72² = 441 + 5184 = 5625, so the hypotenuse is √5625 = 75.
A right triangle has legs of length 30 and 72. What is the length of the hypotenuse?
By the Pythagorean theorem: 30² + 72² = 900 + 5184 = 6084, so the hypotenuse is √6084 = 78.
A right triangle has legs of length 20 and 48. What is the length of the hypotenuse?
By the Pythagorean theorem: 20² + 48² = 400 + 2304 = 2704, so the hypotenuse is √2704 = 52.
A right triangle has a leg of length 18 and a hypotenuse of length 30. What is the length of the other leg?
By the Pythagorean theorem: 30² − 18² = 900 − 324 = 576, so the other leg is √576 = 24.