弦长L=9米弧高H=2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)
=2/2+9^2/(8*2)
=6.0625米
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((9/2)/6.0625)
=95.85度
=95.85*PI/180
=1.6729弧度
C=R*A=6.0625*1.6729=10.142米
弦长L=9米弧高H=2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)
=2/2+9^2/(8*2)
=6.0625米
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((9/2)/6.0625)
=95.85度
=95.85*PI/180
=1.6729弧度
C=R*A=6.0625*1.6729=10.142米