题目

圆弧计算：弦长15.7m,弦高15m,半径9.55,求弧长?弦长0.6m,弦高0.6m,半径0.38m,求弧长?
帮我算下,我怎么算都错

提问时间：2021-03-05

答案

弦长L=15.7m,弦高H=15m,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*H*R+H^2+L^2/4
2*H*R=H^2+L^2/4
R=H/2+L^2/(8*H)
=15/2+15.7^2/(8*15)
=9.554m
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((15.7/2)/9.554)
=110.498度
C=PI*R*A/180=PI*9.554*110.498/180=18.4256m
弦长L=0.6m,弦高H=0.6m,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*H*R+H^2+L^2/4
2*H*R=H^2+L^2/4
R=H/2+L^2/(8*H)
=0.6/2+0.6^2/(8*0.6)
=0.375m
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((0.6/2)/0.375)
=106.26度
C=PI*R*A/180=PI*0.375*106.26/180=0.6955m