Law of Sines Calculator
MathSolve a triangle for its remaining side and angle given one side and two angles, using the law of sines.
Side b
The side opposite angle beta, found via a/sin(alpha) = b/sin(beta).
Angle gamma (degrees)
90.0000
The third angle, since all three angles of a triangle sum to 180 degrees.
Side c
2.0000
The side opposite angle gamma, found via a/sin(alpha) = c/sin(gamma).
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Frequently Asked Questions
What is the law of sines?
For any triangle, the ratio of a side's length to the sine of its opposite angle is the same for all three sides: a/sin(alpha) = b/sin(beta) = c/sin(gamma).
When can the law of sines be used?
It works for any triangle, not just right triangles, as long as you know one side and its opposite angle, plus one more angle or side to solve for the rest.
What if alpha and beta add up to more than 180 degrees?
That is not a valid triangle, since gamma (180 - alpha - beta) would come out zero or negative. Always check that the two given angles leave a positive amount for the third.
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