Law of Sines Calculator
How It Works
This law of sines calculator uses established formulas to provide accurate results.
The basic rule:
- a/sin(A) = b/sin(B) = c/sin(C)
- b = a × sin(B) / sin(A)
- C = 180° - A - B
- Area = ½bc·sin(A)
Results are estimates. Consult a professional for critical decisions.
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Explore Allday Everyday Math →Frequently Asked Questions
What is the Law of Sines?
The Law of Sines states that in any triangle, the ratio of a side to the sine of its opposite angle is constant: a/sin(A) = b/sin(B) = c/sin(C). It is used to solve triangles when you know an angle-side pair plus one additional measurement.
When should I use the Law of Sines?
Use the Law of Sines when you know: (1) Two angles and one side (AAS or ASA), or (2) Two sides and a non-included angle (SSA, the ambiguous case). For SAS or SSS problems, use the Law of Cosines instead.
What is the ambiguous case?
The ambiguous case (SSA) arises when you know two sides and a non-included angle. Depending on the values, there may be zero, one, or two valid triangles. Check if sin(B) = b·sin(A)/a yields a valid sine value.
Can I solve a right triangle with the Law of Sines?
Yes, but for right triangles, SOH CAH TOA and the Pythagorean theorem are simpler. The Law of Sines is most useful for oblique (non-right) triangles.