算弧长 弦长10300,弦距离弧650,

题目

算弧长 弦长10300,弦距离弧650,

答案

弦长L=10300,弦距离弧H=650,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)
=650/2+10300^2/(8*650)
=20726.923
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((10300/2)/20726.923)
=28.77度
=28.77*PI/180
=0.502199弧度
C=R*A=20726.923*0.502199=10409