Question

已知弦长和弦高怎么计算弧长

已知弦长28.1cm,弦高1.3cm怎么计算出弧长是多少!

Answer 1

已知弦长L=28.1cm,弦高H=1.3cm怎么计算出弧长C是多少?
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)
=1.3/2+28.1^2/(8*1.3)
=76.57cm
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((28.1/2)/76.57)
=21.145度
=21.145*PI/180
=0.369056弧度
C=A*R=0.369056*76.57=28.26cm

Answer 2

弦长a,弦高b,弧度2x,半径r
(a/2)*+(r-b)*=r*;
cosx=a/(2r);
弧长=rx
代入求值.