Start with the right angle
If a figure or a sentence says that one angle is 90°, do not open the law of sines first. The right triangle calculator uses the Pythagorean theorem when two sides are known, and the sine, cosine, or tangent ratio when one acute angle is known with a side. Those identities are shorter than the general sine ratio, and they refuse a leg that is longer than the hypotenuse.
Relabel if you must. The right-triangle page keeps the right angle at C. If the book places the right angle at A, swap letters so that C is 90° before you type.
Two angles and a side: AAS or ASA
Two angles determine the third, because the interior angles add to 180°. Any one side then scales the triangle. That is a comfortable case for the law of sines calculator. The angle-sum page can find the missing angle first if you want that step in isolation.
Two sides and the included angle: SAS
The included angle sits between the two known sides. The law of sines does not start from that arrangement, because you do not yet have a side opposite a known angle. Use the law of cosines calculator to find the third side. After that side exists, the sine ratio can finish the remaining angles if you prefer it.
Three sides: SSS
Three sides are also a cosine case. The law of cosines finds an angle; the angle sum or a second cosine application finds the rest. There is no ambiguous extra triangle in SSS. If you only need the area, skip the angles and open the triangle area calculator on Heron’s formula.
Two sides and a non-included angle: SSA
This is the delicate case. One angle, the side opposite that angle, and one extra side can produce no triangle, one triangle, or two triangles. The law of sines still applies, but the height test decides how many solutions survive. Read the ambiguous-case guide before you trust a single answer from a textbook key.
When you want the area
If you already have two sides and the included angle, the sine-area formula is enough. If you have three sides, Heron is enough. You do not need to solve for every angle first. If the homework still asks for the angles, solve the triangle on the matching page, then compute the area as a check.