How it works

Quickly find a missing side or angle in a triangle using the Law of Sines. Just input three known values and let the calculator do the work for your geometry problems.

The Formula

The Law of Sines states that the ratio of a side length to the sine of its opposite angle is constant for all sides and angles in a triangle: a / sin(A) = b / sin(B) = c / sin(C)

Worked Example

1. Example: Finding a Missing Side (AAS)

   Imagine a triangle where Angle A = 30°, Side a = 10 units, and Angle B = 45°. We want to find Side b. Using the Law of Sines: a / sin(A) = b / sin(B) 10 / sin(30°) = b / sin(45°) 10 / 0.5 = b / 0.7071 20 = b / 0.7071 b = 20 * 0.7071 b ≈ 14.142 units Input Angle A = 30, Side a = 10, Angle B = 45 into the calculator to get this result.

Tips, Assumptions & Limitations

• Enter exactly three values to solve for the fourth.
• Angles must be in degrees and less than 180°.
• Side lengths must be positive.
• Be aware of the 'ambiguous case' (SSA) when solving for an angle, as there might be two possible solutions.