已知弦长L=6.5米,弦高H=1米,求对应弧长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)
=1/2+6.5^2/(8*1)
=5.78125米
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((6.5/2)/5.78125)
=68.41度
C=π*R*A/180=π*5.78125*68.41/180=6.9028米
已知弦长L=6.5米,弦高H=1米,求对应弧长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)
=1/2+6.5^2/(8*1)
=5.78125米
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((6.5/2)/5.78125)
=68.41度
C=π*R*A/180=π*5.78125*68.41/180=6.9028米