已知弦长L=20米高H=4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)
=4/2+20^2/(8*4)
=14.5米]
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((20/2)/14.5)
=87.2度
C=PI*R*A/180=PI*14.5*87.2/180=22.069米
已知弦长L=20米高H=4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)
=4/2+20^2/(8*4)
=14.5米]
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((20/2)/14.5)
=87.2度
C=PI*R*A/180=PI*14.5*87.2/180=22.069米