已知弦长和弦高怎么计算弧长?弦长118,
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已知弦长和弦高怎么计算弧长?弦长118,
![已知弦长和弦高怎么计算弧长?弦长118,](/uploads/image/z/7205527-55-7.jpg?t=%E5%B7%B2%E7%9F%A5%E5%BC%A6%E9%95%BF%E5%92%8C%E5%BC%A6%E9%AB%98%E6%80%8E%E4%B9%88%E8%AE%A1%E7%AE%97%E5%BC%A7%E9%95%BF%3F%E5%BC%A6%E9%95%BF118%2C)
已知弦长和弦高怎么计算弧长C?弦长L=118,弦高H=21.
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)
=21/2+118^2/(8*21)
=93.381
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((118/2)/93.381)
=78.37度
=78.37*PI/180
=1.367799弧度
C=R*A=93.381*1.367799=127.726
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)
=21/2+118^2/(8*21)
=93.381
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((118/2)/93.381)
=78.37度
=78.37*PI/180
=1.367799弧度
C=R*A=93.381*1.367799=127.726