已知弦长L=4.5米,弦高H=2米,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)
=2/2+4.5^2/(8*2)
=2.2656米
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((4.5/2)/2.2656)
=166.53度
C=PI*R*A/180=PI*2.2656*166.53/180=6.585米
已知弦长L=4.5米,弦高H=2米,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)
=2/2+4.5^2/(8*2)
=2.2656米
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((4.5/2)/2.2656)
=166.53度
C=PI*R*A/180=PI*2.2656*166.53/180=6.585米