The Pythagorean theorem t is used to find missing side lengths in a right triangle. How do you solve for b, in terms of c and a?

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Answer 1 · 2016-10-19T00:36:56

$b = sqrt(c^2-a^2)$

Given a right triangle with legs of length $a$ and $b$ and hypotenuse of length $c$ , the Pythagorean theorem states that

$a^2 + b^2 = c^2$

Solving for $b$ :

$b^2 = c^2 - a^2$

$=> b = +-sqrt(c^2-a^2)$

However, we know that as a length, $b > 0$ , so we can throw out the negative result. This leaves us with our answer:

$b = sqrt(c^2-a^2)$