Law of Sines Calculator
Solve any triangle using the law of sines. Enter a known side, its opposite angle, and one other angle to calculate all remaining sides, angles, and the area of the triangle.
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). This relationship allows you to find unknown sides or angles when you know at least one side-angle pair and one additional piece of information.
This calculator handles the AAS (angle-angle-side) case, where you know two angles and a non-included side. Since the three angles of a triangle sum to 180 degrees, knowing two angles immediately gives you the third. Then the law of sines finds the remaining sides.
The law of sines is particularly useful in surveying (triangulation), navigation (finding distances to landmarks), astronomy (calculating stellar distances), and engineering (structural analysis). When combined with the law of cosines, it can solve any triangle completely.