How to find the angle of a triangle with 3 sides?

Explanation:

The Law of Cosines specifies the relationship between the three sides of a triangle and any one of the angles. If the sides are designated a, b, and c, and the angle opposite side c is C, then it tells you ...

  c² = a² + b² -2ab·cos(C)

This relationship can be used to find any and all angles, given the three sides of a triangle. Or, having found one angle using the Law of Cosines, the others can be found using the Law of Sines:

  sin(A)/a = sin(B)/b = sin(C)/c

Typically, inverse functions are required. That is, from the Law of Cosines, ...

  C = arccos((a² +b² -c²)/(2ab))

And from the Law of Sines, ...

  A = arcsin(a/c·sin(C))

  B = arcsin(b/c·sin(C))

Note on solving triangles

It often works best to make use of exact values where possible. It is also a good idea to start with the longest side/largest angle. Of course, once you have two angles the other can be found as the supplement of their sum.

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step-by-step explanation: lol