How this calculator works
With two perpendicular legs, the diagonal follows from the Pythagorean theorem. With an acute angle, the opposite leg uses sine and the adjacent leg uses cosine. Area and a leg first recover the other leg. Perimeter and a leg also determine a unique positive right triangle when the perimeter exceeds twice that leg. Use this tool only when the included corner is known to be 90°.
Formula
c=√(a²+b²); c=a/sin A=b/cos A; ab=2K; P=a+b+c. With P and a: b=P(P-2a)/[2(P-a)].
Worked example
Perpendicular runs of 8 ft and 15 ft need a diagonal of 17 ft. A leg opposite a 30° angle that measures 5 cm gives a hypotenuse of 5/sin 30°=10 cm.
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Frequently asked questions
Is the hypotenuse always the longest side?
Yes. Both legs are positive, so c exceeds either leg individually. The extra-length readout compares it with the longer leg.
Can I enter the angle beside the known leg?
Yes. For angle A, a is opposite and b is adjacent. Choose the matching mode or use the complementary angle B.
What if I only know area?
That alone does not fix the shape. Add a leg length or an acute angle to determine the hypotenuse.