The law of cosines is c² = a² + b² − 2ab cos C. Use it when the triangle is not a right triangle and you have two sides and the included angle, or all three sides. If the angle is 90°, cos 90° is 0 and this becomes Pythagorean. The other non-right tool is the law of sines.
When to reach for it
SAS or SSS. Right triangles still want Pythagorean or SOH-CAH-TOA, in SOH-CAH-TOA. Triangle questions as a set are in triangle problems.
The identity sin² + cos² = 1 can still help with a leftover trig value, in sin squared plus cos squared.
The bottom line
Not a right triangle, and you have two sides wrapping an angle: law of cosines.
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