Geometry & TrigonometryHard
Right triangles and trigonometry
Use the Pythagorean theorem and SOH-CAH-TOA to find missing sides and angles in right triangles.
Sample SAT Problem
In a right triangle, the legs are 5 and 12. What is the hypotenuse?
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Step-by-Step Solution
c = √(5² + 12²) = √(25 + 144) = √169 = 13.
Key Tips from Pamela
- SOH: sin = opposite/hypotenuse. CAH: cos = adjacent/hypotenuse. TOA: tan = opposite/adjacent.
- Common Pythagorean triples: 3-4-5, 5-12-13, 8-15-17.
- sin(θ) = cos(90° − θ) — use this for complementary angle problems.
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