Can you find x using the trigonometry of circle sectors?

In summary, a circle sector is a region of a circle bounded by two radii and an arc. Its area can be found using the formula A = (1/2) * r^2 * θ, where r is the radius and θ is the central angle in radians. The length of an arc in a sector can be calculated with the formula L = r * θ. A circle sector is related to a triangle, with the central angle of the sector corresponding to the angle of the triangle and the radius of the circle acting as the hypotenuse. Trigonometry of circle sector has many real-life applications, including in engineering, architecture, physics, navigation, and map-making. It is used to calculate areas and
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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:

\(\displaystyle s=r\theta\)

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. ;)
 

FAQ: Can you find x using the trigonometry of circle sectors?

What is a circle sector in trigonometry?

A circle sector is a region bounded by two radii and an arc of a circle. It is essentially a pie-shaped slice of a circle.

What is the formula for the area of a circle sector?

The formula for finding the area of a circle sector is A = (1/2) * r^2 * θ, where r is the radius of the circle and θ is the central angle of the sector in radians.

How do you find the length of an arc in a circle sector?

To find the length of an arc in a circle sector, you can use the formula L = r * θ, where r is the radius of the circle and θ is the central angle of the sector in radians.

What is the relationship between a circle sector and a triangle in trigonometry?

A circle sector can be thought of as a portion of a circle that is also a triangle with one curved side. The central angle of the sector corresponds to the angle of the triangle, and the radius of the circle is the hypotenuse of the triangle.

How is trigonometry of circle sector used in real life?

Trigonometry of circle sector is used in various fields such as engineering, architecture, and physics. It is used to calculate the area and perimeter of circular objects, determine the angle of rotation in machinery, and analyze the motion of objects on a circular path. It is also used in navigation and map-making to calculate distances and angles between points on a curved surface.

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