弦长L=23米,弧高H=9.4米,求弧长C?
弧半径为R,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)
=9.4/2+23^2/(8*9.4)
=11.735米
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((23/2)/11.735)
=157.05度
=157.05*PI/180
=2.741弧度
C=A*R
=2.741*11.735
=32.165米
弧长C=32.165米