Sector angle and segment area just given only 2 variables ?

In summary, a sector angle is the central angle formed by two radii of a circle, measured in degrees from 0 to 360 degrees. A segment area is the region enclosed by a chord and an arc of a circle, measured in square units. The two variables needed to calculate sector angle and segment area are the radius of the circle and the length of the chord. To calculate the sector angle, you can use the formula: sector angle = (length of arc / circumference of circle) * 360 degrees. To calculate the segment area, you can use the formula: segment area = (sector angle / 360 degrees) * π * (radius)^2 - (1/2) * (radius) * (length of
  • #1
CGUE
23
0
Is there a way to calculate the sector angle and segment area of a circle just given only the radius and the length of the circle ?
So far I can only calculate the sagitta length using the radius and length of the chord i.e.

[tex]S = r - \sqrt{r^2 - \frac{1}{2}l^2}[/tex]

Where r is the radius of the circle and l is the length of the chord.
 
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  • #2
Hi CGUE ! :smile:

sin = opp/hyp …

sin 1/2 sector angle = 1/2 l/r :smile:
 

FAQ: Sector angle and segment area just given only 2 variables ?

What is a sector angle?

A sector angle is the measurement of the central angle formed by two radii of a circle that intersect at the center of the circle. It is measured in degrees and can range from 0 to 360 degrees.

What is a segment area?

A segment area is the region enclosed by a chord and an arc of a circle. It is measured in square units and can be calculated by subtracting the area of the triangle formed by the two radii and the chord from the area of the sector formed by the two radii.

What are the 2 variables needed to calculate sector angle and segment area?

The two variables needed are the radius of the circle and the length of the chord.

How do you calculate sector angle?

To calculate the sector angle, you can use the formula: sector angle = (length of arc / circumference of circle) * 360 degrees

How do you calculate segment area?

To calculate the segment area, you can use the formula: segment area = (sector angle / 360 degrees) * π * (radius)^2 - (1/2) * (radius) * (length of chord) * sin(sector angle)

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