已知弦长L=40cm,弧高H=25cm,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)
=25/2+40^2/(8*25)
=20.5cm
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((40/2)/20.5)
=154.639度
C=PI*R*A/180=PI*20.5*154.639/180=55.329cm
已知弦长40cm,弧高25cm,求弧长.