suppose a triangle has two sides of length 32 and 35, and that the angle between these two sides is 120. Which equation should you solve to find the length of the third side of the triangle

  x² = 32² +35² -2·32·35·cos(120°)

Step-by-step explanation:

The equation of choice is the one that makes use of the law of cosines. If x represents the unknown side, then you would want to solve ...

  x² = 32² +35² -2·32·35·cos(120°)

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The solution is ...

  x² = 3369

  x = √3369 ≈ 58.043

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Comment on the question

Usually, when the question asks, "Which ...", there will be a selection of answer choices. Those will give a clue as to what variables are used, how far the equation is simplified, and whether the equation is for x² or for x. That information is not provided here, so we have shown the equation we would use to solve the problem.