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Here is the problem: Find all three angles of a triangle with sides 4, 4 and 7.

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SSS: find all three angles.

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Check the triangle inequality. 4 plus 4 equals 8 greater than 7, 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 28.955024°, B approximately 28.955024°, C approximately 122.08995°.

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The triangle has sides a equals 4, b equals 4, c equals 7 and angles A approximately 28.955024°, B approximately 28.955024°, C approximately 122.08995°. It is an obtuse isosceles triangle with area approximately 6.7777209 and perimeter approximately 15.

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A plus B plus C equals 180°.

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Heron prime s formula gives the same area: 6.7777209.

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Law of sines ratios: a/sin A approximately 8.2623645, b/sin B approximately 8.2623645, c/sin C approximately 8.2623645.