知道弦长是L=18.5,弓高H=4.6,求弓形面积S?
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)
=4.6/2+18.5^2/(8*4.6)
=11.6
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((18.5/2)/11.6)
=105.764度
S=PI*R^2*A/360-(L*R*COS(A/2))/2
=PI*11.6^2*105.764/360-(18.5*11.6*COS(105.764/2))/2
=59.449