WEBVTT

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Here is the problem: Solve the triangle with a equals 5, b equals 8 and included angle C equals 40°.

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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 5, b equals 8, c equals 5.264640971; A equals 37.62394377°, B equals 102.3760562°, C equals 40°; area equals 12.85575219, perimeter equals 18.26464097.

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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 8.190327398 equals c/sin C equals 8.190327398.