Question

已知拱高弦长求弧长我有4个尺寸帮我求弧长,在知道里面看到公式由于文化底看不懂,请帮我直接算结果.弦长2404拱高664弦

Answer 1

已知拱高H=664弦长L=2404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)

=664/2+2404^2/(8*664)

=1419.95

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

=2*ARC SIN((2404/2)/1419.95)

=115.667度

C=PI*R*A/180=PI*1419.95*115.667/180=2866.57

已知拱高H=669弦长L=1340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)

=669/2+1340^2/(8*669)

=670

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

=2*ARC SIN((1340/2)/670)

=179.83度

C=PI*R*A/180=PI*670*179.83/180=2102.87