已知弦长2060弦高770求弧长.另一个弦长2660弦高770,求弧长.列出公式、计算过程.

Question

已知弦长2060弦高770求弧长.另一个弦长2660弦高770,求弧长.列出公式、计算过程.

Answer 1

已知弦长L=2060弦高H=770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)
=770/2+2060^2/(8*770)
=1073.896
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((2060/2)/1073.896)
=147.123度
C=π*R*A/180=π*1073.896*147.123/180=2757.533
已知弦长L=2660弦高H=770,求弧长C?
弧半径为R,弧所对的圆心角为A.
R=H/2+L^2/(8*H)
=770/2+2660^2/(8*770)
=1533.636
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((2660/2)/1533.636)
=120.274度
C=π*R*A/180=π*1533.636*120.274/180=3219.384