WEBVTT

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Here is the problem: Solve the triangle with a equals 12, b equals 9 and included angle C equals 110°.

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Side a is opposite angle A, b opposite B and c opposite C. This is the SAS case.

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Side c from the law of cosines.

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Other angles from the law of cosines. The law of cosines avoids the sine ambiguity for obtuse angles.

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Area and perimeter.

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So the answer is a equals 12, b equals 9, c equals 17.28804069; A equals 40.71227504°, B equals 29.28772496°, C equals 110°; area equals 50.74340152, perimeter equals 38.28804069.

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Three measurements including a side normally fix a triangle. Two sides with a non-included angle (SSA) can give zero, one or two triangles.

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Triangle 1: angles sum to 180°; a/sin A equals 18.39754863 equals c/sin C equals 18.39754863.