How this calculator works
Two independent measurements, including a size, determine a right triangle. Two sides give the missing side through Pythagoras and the acute angles through atan2. A side and an acute angle give the other lengths using trig ratios. The ratio table makes the opposite-versus-adjacent exchange visible when switching from A to B. Area plus hypotenuse determines two label assignments unless the legs are equal.
Formula
c²=a²+b²; A=atan2(a,b); B=90°-A; sin A=a/c; cos A=b/c; tan A=a/b; K=ab/2.
Worked example
A right triangle with a=5 m and c=13 m has b=12 m, A≈22.619865° and B≈67.380135°. Its sine ratios are 5/13 at A and 12/13 at B.
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Frequently asked questions
Can I solve from two angles only?
No. The two acute angles fix shape but not scale. A length or area is needed as well.
Which angle belongs with a side?
Lowercase a is opposite uppercase A, and b is opposite B. The hypotenuse c is opposite C=90°.
Why use atan2 for the angles?
It uses both legs and returns the appropriate first-quadrant angle without needing to round a side ratio first.