Right Triangles and Pythagorean Theorem

SAT Math · Axiom Academy

Right Triangles & Pythagorean Theorem Master the Pythagorean theorem, special right triangles, and Pythagorean triples that appear frequently on the SAT. In this lesson, you'll master: The Pythagorean theorem and when to use it 30-60-90 triangle ratios and shortcuts 45-45-90 triangle ratios and shortcuts Common Pythagorean triples that appear on the SAT How to quickly identify special right triangles without calculation In any right triangle with legs a and b and hypotenuse c : The hypotenuse is the side opposite the right angle (the longest side). A right triangle has legs of length 5 and 12. What is the length of the hypotenuse? a^2 + b^2 = c^2 5^2 + 12^2 = c^2 25 + 144 = c^2 169 = c^2 c = 13 A Pythagorean triple is a set of three positive integers that satisfy a^2 + b^2 = c^2 . The SAT loves these because you can find answers instantly without using the theorem. In a right triangle, the legs are 6 and 8. Without a calculator, find the hypotenuse. Legs 6 and 8 are and , which is a multiple of the 3-4-5 triple. So the hypotenuse is . A 45-45-90 triangle is an isosceles right triangle (two equal legs, one 90° angle, two 45° angles). In a 45-45-90 triangle, each leg has length 5. What is the hypotenuse? If legs = x = 5 , then hypotenuse = A 30-60-90 triangle has angles of 30°, 60°, and 90°. This is the most common special right triangle on standardized tests. In a 30-60-90 triangle, the side opposite the 30° angle is 4. Find the other two sides.

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