弓形的弦长为L=2*2^0.5cm,高为H=2-2^0.5cm,则弓形的弧长为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)
=(2-2^0.5)/2+(2*2^0.5)^2/(8*(2-2^0.5))
=2cm
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((2*2^0.5/2)/2)
=90度
=90*PI/180
=1.570797弧度
C=R*A=2*1.570797=3.142cm