弦长L=6.7米,弦的中心到弧顶H=0.6米,求圆半径R和这个弧形的面积S?
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)
=0.6/2+6.7^2/(8*0.6)
=9.652米
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((6.7/2)/9.652)
=41.98度
S=PI*R^2*A/360
=PI*9.652^2*41.98/360
=32.041平方米