弓形弧长 已知弦长197,求弧长?
问题描述：
弓形弧长 已知弦长197,求弧长?
答
已知弦长L=197,高H=18,求弧长C?
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)
=18/2+197^2/(8*18)
=278.507
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((197/2)/278.507)
=41.424度
=41.424*PI/180
=0.722987弧度
C=R*A=278.507*0.722987=201.357