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If you mean an angle of 60 degrees opposite a side of 8 cm and has another side called b which is 9 cm then label the angles as A B C and the opposite sides a b c.

This is an ambiguous scenario in which 60 degrees is not the 'included angle' but by manipulating the trigonometrical sine rule the angles are 60 degrees, 103 degrees and 17 degrees or 60 degrees, 77 degrees and 43 degrees.

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Q: What are the possible angles of a triangle when an angle of 60 degrees is opposie side a which is 8 cm and when side b is 9 cm?
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