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keisanHigh-precision calculations for everyday life and work

Area of a Segment (from the chord length and height)

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Calculate the area of a segment, the central angle and length of an arc, and the radius based on the segment’s chord length and height.
Chord Length c
Height of the segment: h
Area S 
Central angle θ rad
= Degrees
Arc Length L 
Radius r 
\(\normalsize Arch\\ (1)\ center\ angle:\hspace{8px} \theta=2\cos^{\tiny-1}(1-{\large\frac{h}{r}})\\ (2)\ circular\ arc :\ L=r\theta\\ (3)\ chord :\hspace{60px} c=2\sqrt{h(2r-h)}\\ (4)\ area:\hspace{67px} S={\large\frac{\theta}{2}}r^{2}-(r-h)\sqrt{h(2r-h)}\\\)

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