弦长L=15米,拱高H=2.5米.求弧长C是多少?
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)
=2.5/2+15^2/(8*2.5)
=12.5米
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((15/2)/12.5)
=73.74度
=73.74*PI/180
=1.287弧度
C=R*A=12.5*1.687=16.088米
弦长L=15米,拱高H=2.5米.求弧长C是多少?
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)
=2.5/2+15^2/(8*2.5)
=12.5米
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((15/2)/12.5)
=73.74度
=73.74*PI/180
=1.287弧度
C=R*A=12.5*1.687=16.088米