弦长L=3.5米,弦中心到弧顶高H=40厘米,求弧长C?急用
弧半径为R,弧所对的圆心角为A.
H=40厘米=0.4米
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)
=0.4/2+3.5^2/(8*0.4)
=4.028米
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((3.5/2)/4.028)
=51.5度
C=PI*R*A/180=PI*4.028*51.5/180=3.621米