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Calculating the hypotenuse [ edit source ] The length of the hypotenuse can be calculated using the square root function implied by the Pythagorean theorem . Using the common notation that the length of the two legs of the triangle (the sides perpendicular to each other) are a and b and that of the hypotenuse is c , we have {\displaystyle c={\sqrt {a^{2}+b^{2}}}.} The Pythagorean theorem, and hence this length, can also be derived from the law of cosines by observing that the angle opposite the hypotenuse is 90° and noting that its cosine is 0: {\displaystyle c^{2}=a^{2}+b^{2}-2ab\cos 90^{\circ }=a^{2}+b^{2}\therefore c={\sqrt {a^{2}+b^{2}}}.} Many computer languages support the ISO C standard function hypot( x , y ), which returns the value above. [5] The function is designed not to fail where the straightforward calculation might overflow or underflow and can be slightly more accurate and sometimes significantly ...