已知弦长2301,弦高261,求弧长,

题目

已知弦长2301,弦高261,求弧长,

答案

已知弦长L=2301,弦高H=261,求弧长C?
弧的半径为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)
=261/2+2301^2/(8*261)
=2666.228
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((2301/2)/2666.228)
=51.127度
=51.127*PI/180
=0.89233弧度
C=A*R
=0.89233*2666.228
=2379.15