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Here is the problem: Find all three angles of a triangle with sides 3, 4 and 5.

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SSS: find all three angles.

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Check the triangle inequality. 3 plus 4 equals 7 greater than 5, so a triangle exists.

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Angle C (opposite side c).

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Angle A (opposite side a).

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Third angle from the angle sum.

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Area from two sides and the included angle.

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So the answer is A approximately 36.869898°, B approximately 53.130102°, C approximately 90°.

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The triangle has sides a equals 3, b equals 4, c equals 5 and angles A approximately 36.869898°, B approximately 53.130102°, C approximately 90°. It is a right scalene triangle with area approximately 6 and perimeter approximately 12.

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A plus B plus C equals 180°.

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Heron prime s formula gives the same area: 6.

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Law of sines ratios: a/sin A approximately 5, b/sin B approximately 5, c/sin C approximately 5.