The Pythagorean theorem
The theorem applies exclusively to right triangles, which have one 90-degree interior angle. The two shorter sides meeting at the right angle are called legs and are labelled a and b. The longest side, opposite the right angle, is the hypotenuse c. Knowing any two sides allows the third to be calculated exactly using the theorem.
To find a missing leg, rearrange the formula. If the hypotenuse c and leg b are known, leg a equals the square root of (c squared minus b squared). If the two legs are known, the hypotenuse is the square root of their sum of squares. Common integer solutions are called Pythagorean triples; the 3-4-5 right triangle is the simplest example, where 9 + 16 = 25.
c^2 = a^2 + b^2
The square of the hypotenuse equals the sum of the squares of the two legs.
a = sqrt(c^2 - b^2) or b = sqrt(c^2 - a^2)
Rearranged forms for finding a missing leg when the hypotenuse and the other leg are known.
Area = 0.5 x a x b
The area of a right triangle is half the product of its two legs.
Perimeter = a + b + c
The perimeter is the sum of all three sides.