The calculator uses the law of sines to finish a triangle when you know AAS, ASA, or SSA. You enter the known sides and angles. The result lists every missing part and the arithmetic that produced it. If two triangles fit the SSA data, both solutions appear.
Known parts
Leave a box empty when that part is unknown. The side labeled a sits opposite angle A.
Lesson: when the law of sines is enough
The law of sines says that each side of a triangle is proportional to the sine of the opposite angle. Once one pair (a side and its opposite angle) is known, the common ratio fixes every other pair.
AAS and ASA are comfortable cases. Two angles determine the third because the angle sum is 180°. Any one side then scales the triangle. SSA is different: one angle, the side opposite that angle, and one extra side can produce no triangle, one triangle, or two triangles. The two-triangle outcome is the ambiguous case. A short guide on the ambiguous case walks through the height test.
This page does not solve SSS or SAS with the sine ratio alone. Those arrangements start from the law of cosines. The calculator also rejects a side of 0, a negative length, and an angle that is not strictly between 0° and 180°.
Practice problems
1. AAS
Angle A is 40°, angle B is 60°, and the side opposite A is 8. Find the remaining parts.
2. ASA
Angle A is 35°, angle C is 75°, and side b is 12. Find the remaining parts.
3. SSA
Angle A is 40°, the side opposite A is 6, and side b is 8. Decide whether the triangle is unique.
Show answers
Problem 1. Angle C is 80°. Side b is about 10.777, and side c is about 12.257.
Problem 2. Angle B is 70°. The side opposite A is about 7.325, and side c is about 12.335.
Problem 3. This is the ambiguous case. Triangle 1 has B about 59.0°, C about 81.0°, and c about 9.20. Triangle 2 has B about 121.0°, C about 19.0°, and c about 3.03.