已知弦长6.5米,求弧长
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已知弦长6.5米,求弧长
![已知弦长6.5米,求弧长](/uploads/image/z/10923021-45-1.jpg?t=%E5%B7%B2%E7%9F%A5%E5%BC%A6%E9%95%BF6.5%E7%B1%B3%2C%E6%B1%82%E5%BC%A7%E9%95%BF)
已知弦长L=6.5米,拱高H=1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)
=1/2+6.5^2/(8*1)
=5.78125米
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((6.5/2)/5.78125)
=68.41度
=68.41*PI/180
=1.193996弧度
C=R*A=5.78125*1.193996=6.903米
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)
=1/2+6.5^2/(8*1)
=5.78125米
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((6.5/2)/5.78125)
=68.41度
=68.41*PI/180
=1.193996弧度
C=R*A=5.78125*1.193996=6.903米