Angles involving trigonometric Ratios Worded Problem

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Homework Help Overview

The discussion revolves around a triangle ABC where AC is three times the length of AB, and one angle is given as 120°. Participants are tasked with expressing another angle, BCA, in a specific form. The problem involves trigonometric ratios and the sine rule, with a focus on understanding the relationships between the angles and sides of the triangle.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the application of the sine rule and the labeling of triangle sides and angles. There are attempts to clarify the relationships between the angles and sides, with some questioning the correctness of their initial assumptions and calculations.

Discussion Status

The conversation is ongoing, with participants exploring various interpretations of the sine rule and the relationships between the angles. Some have provided guidance on how to approach the problem, while others express confusion about the labeling and calculations. There is no explicit consensus on the correct approach yet.

Contextual Notes

Participants note that the diagram provided is unclear, which may affect their understanding of the problem. There is also mention of potential errors in angle labeling and the need to clarify the definitions of the sides and angles involved.

  • #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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