弦长是L=10.84米,弦高是H=2.1米,求弦所对应的弧长C?
弧的半径为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)
=2.1/2+10.84^2/(8*2.1)
=8.044米
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((10.84/2)/8.04)
=84.72度
=84.72*PI/180
=1.47858弧度
C=A*R
=1.47858*8.044
=11.894米