Angles involving trigonometric Ratios Worded Problem

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In the discussion about solving a trigonometric problem involving triangle ABC, participants explore the application of the sine rule to find the unknown angle BCA. The triangle has specific angle measures, with angle BAC at 120° and the relationship AC = 3AB. Participants clarify the correct labeling of angles and sides, emphasizing that the sum of angles in a triangle must equal 180°. Confusion arises regarding the correct values for angles and the sine rule's application, particularly the derivation of angle BCA. Ultimately, the conversation focuses on ensuring proper understanding of the sine rule and solving for the unknown angle.
  • #31
I don't think they are wrong. I have ##x:=AB## and thus ##AC=3x## opposite of ##\beta = \angle (ABC) = 60°-\theta ## and ##x=AB## opposite of ##\gamma = \angle (BCA) =\theta##.

You can get rid of ##x## because you're not interested in its value. ##\sin \theta## is what we're looking for.
 

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