Question

弦长600 拱高200求弧长 弦长1000拱高300求弧长 急！！答案要准确

Answer 1

弦长L=600 拱高H=200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)
=200/2+600^2/(8*200)
=325
A=2*ARC SIN((L/2)/R
=2*ARC SIN((600/2)/325
=134.76度
=134.76*PI/180
=2.35201弧度
C=R*A=325*2.35201=764.4

弦长L=1000拱高H=300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)
=300/2+1000^2/(8*300)
=566.67
A=2*ARC SIN((L/2)/R
=2*ARC SIN((1000/2)/566.67
=123.855度
=123.855*PI/180
=2.161678弧度
C=R*A=566.67*2.161678=1224.95