Law of Sines Calculator
Use the law of sines to find an unknown side from an angle-side pair and a second angle, with the full triangle solved.
How it works
a / sin A = b / sin B = c / sin C
The law of sines says every side of a triangle is proportional to the sine of its opposite angle, so the ratio side/sin(angle) is the same for all three pairs. Given one complete side-angle pair plus a second angle, you can find the third angle (angles sum to 180°) and then every remaining side by scaling that common ratio.
Worked example
For angle A = 30°, side a = 10 and angle B = 45°: the ratio a/sin A = 10/0.5 = 20, so side b = 20·sin45° ≈ 14.14. Angle C = 180 − 30 − 45 = 105°, giving side c = 20·sin105° ≈ 19.32.
Sources: Law of sines — Wikipedia
Frequently asked questions
What information does the law of sines need?
A matching angle-and-opposite-side pair, plus one more angle or side. This calculator uses two angles and the side opposite one of them (AAS), which always yields a single triangle.
What is the ambiguous case?
When you know two sides and a non-included angle (SSA), there can be zero, one, or two valid triangles. Using two known angles as here avoids that ambiguity entirely.
Why must the two angles add to less than 180°?
The three angles of a triangle sum to 180°, so the third angle is 180 − A − B. If A and B already reach or exceed 180°, no valid triangle exists.
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This calculator is for educational purposes. Double-check important results before acting on them.