Question

已知弦长4.5米,3米,求弧长.

Answer 1

设弧半径为R,弧所对的圆心角为A,则有：

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)

=1.3/2+4.5^2/(8*1.3)

=2.597米

A=2*ARC SIN((L/2)/R)

=2*ARC SIN((4.5/2)/2.597)

=120.07度

弧长C=PI*R*A/180=PI*2.597*120.07/180=5.443米