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Law of Sines Calculator

Solve triangles with the law of sines: find a missing side or a missing angle from known parts.

Law of Sines

Pick what to find, then enter the known parts.

Result
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Enter numbers to see the result.

Third angle C
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Check a/sinA
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Formula: a/sin A = b/sin B = c/sin C. Side: b = a sin B / sin A. Angle: sin B = b sin A / a.
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Sides track their angles

The law of sines says each side divided by the sine of its opposite angle is the same constant: a/sin A = b/sin B = c/sin C. That constant is the triangle's circumdiameter. Knowing any angle-side pair unlocks the rest of the triangle.

The ambiguous case

Given two sides and a non-included angle (SSA), the sine equation can yield two valid angles: an acute one and its supplement. The tool flags this ambiguity and shows the acute solution with the third angle computed.

Law of Sines FAQs

How do I find side b if A=40 deg, a=7, B=60 deg?
b = 7 x sin 60 / sin 40, about 9.43. The defaults are preloaded in side mode.
What is the law of sines formula?
a/sin A = b/sin B = c/sin C. Each side is proportional to the sine of its opposite angle.
Can the law of sines find an angle?
Yes. Switch to angle mode and enter side a, angle A, and side b; the tool computes B = arcsin(b sin A / a).
Why does it say no triangle exists?
If b sin A / a exceeds 1, no angle has that sine, so the given parts cannot form a triangle.
Is my triangle data uploaded?
No. The trigonometry runs entirely in your browser.
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