Question

In a right triangle the length of a hypotenuse is c and the length of one leg is a, and the length of the other leg is b, what is the value of b, if c=13 and a=12

Answer 1

The Pythagorean theorem tells you ...

... c² = a² + b²

... 13² = 12² + b² . . . . . fill in the given numbers

... 169 - 144 = b² . . . . .subtract 12²

... √25 = b . . . . . . . . . take the square root

... b = 5 . . . . . . The value of b you're looking for.

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The numbers {5, 12, 13} make what is called a "Pythagorean triple" a set of integers that satisfies the relation of the Pythagorean theorem. These, and the triple {3, 4, 5} are often seen in algebra problems. It can be worthwhile to remember these numbers.