Can you find x using the trigonometry of circle sectors?

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    Circle Trigonometry
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SUMMARY

The discussion focuses on solving for the variable x in a circular sector using the formula for arc-length, s = rθ, where r is the radius and θ is the subtended angle. Participants suggest deriving two equations involving x and θ by applying this formula. Additionally, the concept of similarity is introduced to equate the ratio of radius to arc-length for different sectors, providing an alternative method for finding x.

PREREQUISITES
  • Understanding of circular sectors and their properties
  • Familiarity with the formula for arc-length in trigonometry
  • Knowledge of angle measurement in radians
  • Basic principles of similarity in geometry
NEXT STEPS
  • Study the derivation of arc-length formulas in circular geometry
  • Explore the concept of similarity in geometric figures
  • Learn how to apply trigonometric ratios in circular sectors
  • Investigate the relationship between radius, angle, and arc-length in different contexts
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Students studying geometry, mathematics educators, and anyone interested in applying trigonometric principles to solve problems involving circular sectors.

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I need help in solving this problem. Below shows all the measurements of the diagram, I need to find x:View attachment 6590
 

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    Screen Shot 2017-05-08 at 21.41.32.png
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For a circular sector of radius $r$, subtending angle $\theta$, the arc-length $s$ is given by:

$$s=r\theta$$

Can you apply this formula to get two equations in $x$ and $\theta$?

Or, we can use similarity to equate the ratio of radius to arc-length for both sectors. ;)
 

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