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Here is the problem: Two sides of a triangle are 2.5 and 4 with a 35.5° 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 approximately 2.4428855; A approximately 36.461304°, B approximately 108.0387°.

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The triangle has sides a equals 2.5, b equals 4, c approximately 2.4428855 and angles A approximately 36.461304°, B approximately 108.0387°, C approximately 35.5°. It is an obtuse scalene triangle with area approximately 2.9035148 and perimeter approximately 8.9428855.

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A plus B plus C equals 180°.

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Heron prime s formula gives the same area: 2.9035148.

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Law of sines ratios: a/sin A approximately 4.206773, b/sin B approximately 4.206773, c/sin C approximately 4.206773.