已知弦长L=28.57米,弦中点到弧中点的距离为H=3.6米,求弧形面积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)
=3.6/2+28.57^2/(8*3.6)
=30.1418米
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((28.57/2)/30.1418)
=56.579度
S=π*R^2*A/360-(L/2)*R*COS(A/2)
=π*30.1418^2*56.579/360-(28.57/2)*30.1418*COS(56.579/2)
=69.432平方米