WEBVTT

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Here is the problem: Two sides of a triangle are 5 and 7 with a 60° angle between them. Find the third side.

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SAS: find the third side and the remaining angles.

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Substitute into c squared equals a squared plus b squared minus 2ab times cos C.

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Take the square root.

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Find angle A with the law of cosines rearranged.

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Angles of a triangle add to 180°.

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Area from two sides and the included angle.

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So the answer is c equals the square root of 39 approximately 6.244997998; A approximately 43.897886°, B approximately 76.102114°.

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The triangle has sides a equals 5, b equals 7, c approximately 6.244998 and angles A approximately 43.897886°, B approximately 76.102114°, C approximately 60°. It is an acute scalene triangle with area approximately 15.155445 and perimeter approximately 18.244998.

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A plus B plus C equals 180°.

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Heron prime s formula gives the same area: 15.155445.

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Law of sines ratios: a/sin A approximately 7.2111026, b/sin B approximately 7.2111026, c/sin C approximately 7.2111026.