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)#