Sector angle and segment area just given only 2 variables ?

AI Thread Summary
Calculating the sector angle and segment area of a circle requires the radius and the chord length. The sagitta length can be determined using the formula S = r - √(r² - (1/2)l²), where r is the radius and l is the chord length. The sine function is applied to find the half sector angle, using the relationship sin(1/2 sector angle) = (1/2)l/r. This discussion focuses on deriving these values from the given variables. Understanding these calculations can aid in solving problems related to circular segments.
CGUE
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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.

S = r - \sqrt{r^2 - \frac{1}{2}l^2}

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

sin = opp/hyp …

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

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