Special right triangles and Pythagorean triples

Two right triangles appear so often that their side ratios are worth knowing exactly. A 45-45-90 triangle, which is half of a square, has two equal legs, and its hypotenuse is a leg times the square root of 2: legs of 5 give a hypotenuse of 5 times the square root of 2, about 7.07. A 30-60-90 triangle, which is half of an equilateral triangle, has a hypotenuse twice as long as its shorter leg (the one opposite the 30-degree angle), and its longer leg is the shorter leg times the square root of 3: a shorter leg of 4 gives a hypotenuse of 8 and a longer leg of 4 times the square root of 3. These ratios give exact trigonometric values, like sin(30 degrees) = 1/2 and sin(45 degrees) = (square root of 2)/2. Pythagorean triples are whole-number side lengths that satisfy a^2 + b^2 = c^2, like 3-4-5, 5-12-13, 8-15-17, and 7-24-25, and any multiple of a triple, like 6-8-10, is also a triple.

This explanation is AI-generated and can occasionally be wrong. 🚩 Report