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# Solution of Triangles (Ambiguous Cases)

The three sides a, b, c and the three angles A, B, C are called the elements of the triangle ABC. When any three of these six elements (except all the three angles) of a triangle are given, the triangle is known completely; that is, the other three elements can be expressed in terms of the given elements and can be evaluated. This process is called the solution of triangles.
• If the three sides a, b, c are given, angle A is obtained from tan = or cos A = . B and C can be obtained in the similar way.
• If two sides b and c and the included angle A are given, then = cot gives Also , so that B and C can be evaluated. The third side is given by a = or a2 = b2 + c2 â€“ 2bc cos A.
• If two sides b and c and the angle B (opposite to side bare given, then sin C = , A = 180Â° â€“ (B + C) and a = give the remaining elements.