已知弧形的高是H=1.33米,弦长L=5.15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)
=1.33/2+5.15^2/(8*1.33)
=3.158米
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((5.15/2)/3.158)
=109.266度
=109.266*PI/180
=1.907057弧度
C=R*A=3.158*1.907057=6.022米