弦长8.18米,拱高0.78米,求弧长?

2026-05-18 14:26:04
推荐回答(1个)
回答1:

弦长L=8.18米,拱高H=0.78米,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)
=0.78/2+8.18^2/(8*0.78)
=11.113米
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((8.18/2)/11.113)
=43.189度
C=π*R*A/180=π*11.113*43.189/180=8.3769米