Question

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When given all three side lengths of a triangle but none of the angle measures, you can solve for all angle measures using __________.

Answer 1

If you are given with all the tree sides of the triangle, you may solve for all the angles through the Law of Cosines,
c² = a² + b² - 2ab(cos C)
where angle C is the angle opposite the side c. You may use the same equation to get the values of the remaining angle. Additionally, if you already have one known angle, you can solve for the rest of the angles by Law of Sines,
a / sin A = b / sin B = c / sin C