知道弓形的弦长L=18.6m和高度H=3.5m,如何求弧长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*H*R+H^2+L^2/4
2*H*R=H^2+L^2/4
R=H/2+L^2/(8*H)
=3.5/2+18.6^2/(8*3.5)
=14.106m
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((18.6/2)/14.106)
=82.494度
=82.494*PI/180
=1.493794弧度
C=R*A=14.106*1.493794=20.309m