WEBVTT

1
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Here is the problem: Solve the triangle with sides a equals 3, b equals 4, c equals 5.

2
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Side a is opposite angle A, b opposite B and c opposite C. This is the SSS case.

3
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Each angle from the law of cosines.

4
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Area and perimeter.

5
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So the answer is a equals 3, b equals 4, c equals 5; A equals 36.86989765°, B equals 53.13010235°, C equals 90°; area equals 6, perimeter equals 12.

6
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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 5 equals c/sin C equals 5.