已知弧的一边是L=8,弧高H=0.45,怎样算出弧长C?公式?
弧的半径为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)
=0.45/2+8^2/(8*0.45)
=18
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((8/2)/18)
=25.68度
=25.68*PI/180
=0.488弧度
C=A*R
=0.488*18
=8.067米
已知弧的一边是L=8,弧高H=0.45,怎样算出弧长C?公式?
弧的半径为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)
=0.45/2+8^2/(8*0.45)
=18
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((8/2)/18)
=25.68度
=25.68*PI/180
=0.488弧度
C=A*R
=0.488*18
=8.067米