已知一圆的弦长L=229.5米,拱高H=20.5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)
=20.5/2+229.5^2/(8*20.5)
=331.41
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((229.5/2)/331.41)
=40.516度
=40.516*PI/180
=0.70714弧度
C=R*A=331.41*0.70714=234.352米