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Here is the problem: Find all three angles of a triangle with sides 5, 6 and 9.

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SSS: find all three angles.

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Check the triangle inequality. 5 plus 6 equals 11 greater than 9, 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 31.586338°, B approximately 38.942441°, C approximately 109.47122°.

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The triangle has sides a equals 5, b equals 6, c equals 9 and angles A approximately 31.586338°, B approximately 38.942441°, C approximately 109.47122°. It is an obtuse scalene triangle with area approximately 14.142136 and perimeter approximately 20.

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A plus B plus C equals 180°.

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Heron prime s formula gives the same area: 14.142136.

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Law of sines ratios: a/sin A approximately 9.5459415, b/sin B approximately 9.5459415, c/sin C approximately 9.5459415.