已知弦长L=6米,拱高H=0.5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)
=0.5/2+6^2/(8*0.5)
=9.25米
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((6/2)/9.25)
=37.85度
=37.85*PI/180
=0.660595弧度
C=R*A=9.35*0.660595=6.111米