WEBVTT

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Here is the problem: Solve the triangle with a equals 7, b equals 10 and included angle C equals 60°.

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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 7, b equals 10, c equals 8.888194417; A equals 43.00391194°, B equals 76.99608806°, C equals 60°; area equals 30.31088913, perimeter equals 25.88819442.

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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 10.26320288 equals c/sin C equals 10.26320288.