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Several options:

  • Draw it and measure the missing side.
  • Use coordinate geometry. You can draw the base and two of the sides since you know the angles that these lines make and their lengths. You therefore know their upper end points and so calculating the length of the fourth side is trivial.
  • Consider the triangle ABC. Sides AB and BC are known as is angle ABC. So you can use the sine rule to calculate AC and angles CAB and ACB. Angle DAB is known so angle DAC = DAB - CAB, angle ACD = BCD - ACB. In triangle ACD, two angles are known so all three are known. Use the sine rule again to find CD.
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Q: How do you find the unknown side of a quadrilateral with 3 known sides and 4 angles?
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