已知弦长L=7.5米,弦高H=0.8米,求弧长C?
设半径为R,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)
=0.8/2+7.5^2/(8*0.8)
=9.189米
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((7.5/2)/9.189)
=48.17度
=48.17*PI/180
=0.8407弧度
C=A*R
=0.9407*9.189
=7.726米