弦长2200,弧高300,R2166.5求弧长
问题描述：
弦长2200,弧高300,R2166.5求弧长
答
弦长L=2200,弧高H=300,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*R*H+H^2+L^2/4
2*R*H=H^2+L^2/4
R=H/2+L^2/(8*H)
=300/2+2200^2/(8*300)
=2166.67
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((2200/2)/2166.67)
=61.02度
=61.02*PI/180
=1.065弧度
C=A*R=1.065*2166.67=2307.52
弦长L=2200,R=2166.5,求弧长C?
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((2200/2)/2166.5)
=61.03度
=61.03*PI/180
=1.0651弧度
C=A*R=1.0651*2166.5=2307.54