已知弦长1600 拱高354求半径、弧长
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已知弦长1600 拱高354求半径、弧长
![已知弦长1600 拱高354求半径、弧长](/uploads/image/z/1715259-3-9.jpg?t=%E5%B7%B2%E7%9F%A5%E5%BC%A6%E9%95%BF1600+%E6%8B%B1%E9%AB%98354%E6%B1%82%E5%8D%8A%E5%BE%84%E3%80%81%E5%BC%A7%E9%95%BF)
已知弦长L=1600 拱高H=354求半径R、弧长C?
弧所对圆心角为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)
=354/2+1600^2/(8*354)
=1080.95
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((1600/2)/1080.95)
=95.478度
=95.478*PI/180
=1.6664弧度
C=A*R
=1.6664*1080.95
=18041.3
半径R=1080.95、弧长C=18041.3
弧所对圆心角为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)
=354/2+1600^2/(8*354)
=1080.95
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((1600/2)/1080.95)
=95.478度
=95.478*PI/180
=1.6664弧度
C=A*R
=1.6664*1080.95
=18041.3
半径R=1080.95、弧长C=18041.3