Solve any triangle
Choose which three parts you know, then type them in. Side a is opposite angle A, side b is opposite B, side c is opposite C. Angles are in degrees. The demo draws the triangle to scale and writes out the working. Try the last option (SSA), two sides and an angle that is not between them: sometimes it gives two triangles, sometimes none.
In the picture, blue parts are the ones you typed and orange parts were worked out.
What's going on
Two rules solve every triangle. The cosine rule, a² = b² + c² − 2bc cos A, is Pythagoras with a correction term for an angle that is not 90°. Use it when you have three sides, or two sides and the angle between them. The sine rule, a/sin A = b/sin B = c/sin C, says each side is in the same ratio to the sine of the angle facing it. Use it when you know a side and the angle opposite it.
When two angles are known the third is free, because the three add to 180°. That is why ASA and AAS are easy: find the third angle first, then use the sine rule twice.
SSA is the awkward one. The sine rule gives sin B, but two angles between 0° and 180° share each sine: B and 180° − B. Take A less than 90° and picture side a as a rod hinged at C, swinging down towards the base. If it is too short it never reaches (no triangle). If it is at least as long as b it reaches once. In between it reaches the base in two places, and both triangles are real. (When A is 90° or more there is never a second triangle: one if a is longer than b, none otherwise.) Try a = 7, b = 10, A = 40°, then make a smaller until the two triangles merge and disappear.
Sheets: Triangles without a right angle and Mapping a country with one measured line.