Question

圆弧弦长5.1米,玄高80cm,弧长是多少,

Answer 1

圆弧弦长L=5.1米,玄高H=80cm,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)

=0.8/2+5.1^2/(8*0.8)

=4.464米

A=2*ARC SIN((L/2)/R)

=2*ARC SIN((5.1/2)/4.464)

=69.672度

C=PI*R*A/180=PI*4.464*69.672/180=5.428米