MHB Can you find x using the trigonometry of circle sectors?

AI Thread Summary
To find x in the circular sector problem, the arc-length formula \( s = r\theta \) can be applied to derive two equations involving x and the angle \( \theta \). Additionally, the concept of similarity can be utilized to establish a ratio between the radius and arc-length for the sectors. This approach allows for the formulation of equations that can help solve for the unknown variable x. Both methods provide a structured way to tackle the problem using trigonometric principles. Understanding these relationships is key to finding the solution effectively.
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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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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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