Solve a triangle with the law of sines from an angle, its opposite side, and a second angle. Enter the two angles and the side.
Usage Tip
The law of sines is ideal for ASA and AAS triangles; for two sides and an included angle, use the law of cosines.
Every side over the sine of its opposite angle is equal
It solves triangles when you know an angle and its opposite side, plus one more angle or side.
The third angle is 180 minus the other two.
Angles must sum to less than 180 degrees.
The law of sines says that in any triangle the ratio of a side to the sine of its opposite angle is the same for all three sides. With two angles and one side known, the third angle is 180 degrees minus the other two, and each remaining side follows from the ratio.
Because the angles of a triangle add up to 180 degrees, the two angles you enter must add up to less than 180. Make sure the side you enter is the one opposite the angle you label as its partner. The law of sines is used in surveying and navigation to find distances that cannot be measured directly. When you know two sides and an angle that is not between them, the law of sines can have two possible answers, so be careful with that case.