已知它的弦长2360MM和拱高600MM,求弧长是多少最好有公式!已知它的弦长1760MM和拱高600MM,求弧长是多少!

题目

已知它的弦长2360MM和拱高600MM,求弧长是多少最好有公式!已知它的弦长1760MM和拱高600MM,求弧长是多少!

答案

已知它的弦长L=2360MM和拱高H=600MM,求弧长C?
弧的半径为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)
=600/2+2360^2/(8*600)
=1460.3MM
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((2360/2)/1460.3)
=107.81度
=107.81*PI/180
=1.8816弧度
C=A*R
=1.8816*1460.3
=2747.8MM
已知它的弦长L=1760MM和拱高H=600MM,求弧长C
弧的半径为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)
=600/2+1760^2/(8*600)
=945.3MM
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((1760/2)/945.3)
=137.15度
=137.15*PI/180
=2.39368弧度
C=A*R
=2.39368*945.3
=2262.8MM