How does the Law of Sines work?

The ratio a/sin(A) = b/sin(B) = c/sin(C) Then: Use when given: AAS, ASA, or SSA (be careful — SSA can give 0, 1, or 2 solutions).

Can you give an example of how to use the Law of Sines?

Example: Input A=30°, B=45°, a=10 gives a result of b ≈ 14.14 (10/sin30° = b/sin45° → b=10√2).

Is the Law of Sines free to use?

Yes — completely free with no registration, download, or subscription required. All calculations happen instantly in your browser.

How accurate is the Law of Sines?

Our Law of Sines uses verified mathematical formulas and is accurate to multiple decimal places. Results are calculated in real-time using the same methods used by professionals.

Mathematics

Law of Sines

Law of Sines Calculator

Enter side a, angle A (opposite a), and side b to solve the triangle.

Side a

Angle A (°)

Side b

The Law of Sines states that in any triangle, each side divided by the sine of its opposite angle is constant. It is used to solve triangles when you know an angle-side pair plus another angle or side.

Ratio	Form
Basic	a/sin(A) = b/sin(B) = c/sin(C)
Find side b	b = a·sin(B)/sin(A)
Find angle B	sin(B) = b·sin(A)/a

References

›Law of sines — Wikipedia

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Law of Sines

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The ambiguous case (SSA)

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