Law of Sines Calculator

About this tool

What Is the law of sines? Law of Sines Calculator. The law of sines calculator solves a triangle when you know two angles and one side (ASA/AAS), finding the remaining side, the third angle, and the enclosed area. In any triangle the ratio of a side to the sine of its opposite angle is the same for all three corners: a/sin A = b/sin B = c/sin C. This lets one known pair unlock the whole triangle. The law applies to all triangles, right or oblique. Knowing two angles fixes the third because they always sum to 180°; with one side known, the scale is set and both other sides follow. a/sin A = b/sin B = c/sin C, angles summing to 180°. How to Use Enter the two known angles A and B in degrees. Enter the length of the side a opposite angle A. Read side b, angle C, and the triangle's area; the tool also shows a labelled breakdown of each result. Worked Example With A = 45°, B = 45° and a = 10 the triangle is isosceles: b = 10, C = 90°, area = 50. With A = 45°, B = 90°, a = 10 the tool returns b ≈ 14.142 and c ≈ 19.318, correctly handling the right case. Common Use Cases triangulation and bearing problems structural forces on inclined members astronomy 'distance to a star' problems surveying with base-and-angle method Important Notes Angles A and B must be strictly positive and sum below 180°. The side a must be strictly positive and is used as the scale reference. Work happens locally