已知弦长L=30米和弦中到弧最高点H=3.65米,求面积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)
=3.65/2+30^2/(8*3.65)
=32.647米
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((30/2)/32.647)
=54.705度
扇形面积S=PI*R^2*A/360
=PI*32.647^2*54.705/360
=508.81平方米