已知圆弧弦长L=25米,拱高H=1.5米,求弧长C、圆心角A、圆半径R?
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*H*R+H^2+L^2/4
2*H*R=H^2+L^2/4
R=H/2+L^2/(8*H)
=1.5/2+25^2/(8*1.5)
=52.833米
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((25/2)/52.833)
=27.37度
=27.37*PI/180
=0.477716弧度
C=R*A=52.833*0.477716=25.239米