已知弦长L=8拱高H=1.8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)
=1.8/2+8^2/(8*1.8)
=5.344米
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((8/2)/5.344)
=96.91度
C=π*R*A/180=π*5.344*96.91/180=9.04米
已知弦长L=8拱高H=1.8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)
=1.8/2+8^2/(8*1.8)
=5.344米
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((8/2)/5.344)
=96.91度
C=π*R*A/180=π*5.344*96.91/180=9.04米