Solve for missing sides and angles in any triangle using the Law of Sines.
Known Values
Known Reference Pair
Target Pair Member
°
Missing required inputs (a, b, Angle B)
Solution Results
0.00
Result
Results based on the proportional relationship between sides and sines of opposite angles.
Ratio (a/sin A)0
About this calculator
What is the Law of Sines?
The Sine Rule (or Law of Sines) states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant. This allows us to solve for missing sides or angles when we have specific combinations of known information.
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Pro Tips
Use the Law of Sines when you know an angle and its opposite side, plus one other piece of information (AAS, ASA, or SSA).
Be careful with the SSA case, as it can be 'ambiguous' (two possible triangles).
Ensure your calculator is in Degree mode for angle calculations.
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Fun Facts
"The Law of Sines was first formulated in the Islamic world during the 10th century."
"It works for non-right triangles, making it far more versatile than basic SOH CAH TOA."
"The constant ratio a/sin(A) is actually equal to the diameter of the triangle's circumcircle."
