圆弧计算:弦长10.52m,弦高12.84m,求弧长?弦长3m,弦高11.84m,求弧长?

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圆弧计算:弦长10.52m,弦高12.84m,求弧长?弦长3m,弦高11.84m,求弧长?

圆弧计算:弦长10.52m,弦高12.84m,求弧长?弦长3m,弦高11.84m,求弧长?
圆弧计算:弦长10.52m,弦高12.84m,求弧长?弦长3m,弦高11.84m,求弧长?

圆弧计算:弦长10.52m,弦高12.84m,求弧长?弦长3m,弦高11.84m,求弧长?
弦长L=10.52m,弦高H=12.84m,求弧长C?
弧半径为R,弧所对的圆心角为A.
R^2=(R-H)^2+(L/2)^2
R^2=R^2-2*H*R+H^2+L^2/4
2*H*R=H^2+L^2/4
R=H/2+L^2/(8*H)
=12.84/2+10.52^2/(8*12.84)
=7.497m
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((10.52/2)/7.497)
=89.107度
C=PI*R*A/180=PI*7.497*89.107/180=11.66m
弦长L=3m,弦高H=11.84m,求弧长C?
弧半径为R,弧所对的圆心角为A.
R^2=(R-H)^2+(L/2)^2
R^2=R^2-2*H*R+H^2+L^2/4
2*H*R=H^2+L^2/4
R=H/2+L^2/(8*H)
=11.84/2+3^2/(8*11.84)
=6.015m
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((3/2)/6.015)
=28.88度
C=PI*R*A/180=PI*6.015*28.88/180=3.032m