已知弦长L=8.5米,弦高H=1.9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)
=1.9/2+8.5^2/(8*1.9)
=5.7033米
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((8.5/2)/5.7033)
=96.35度
C=PI*R*A/180=PI*5.7033*96.35/180=9.591米