已知弧长L=54,拱高H=10,求弧长C多少?
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)
=10/2+54^2/(8*10)
=41.45
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((54/2)/41.45)
=2*ARC SIN(0.65138721)
=81.29度
C=π*R*A/180=π*41.45*81.29/180=58.81