已知弦長(zhǎng)L=24 弦中點(diǎn)到弧中點(diǎn)是H=2.4 求弧長(zhǎng)C?
弧半徑為R,弧所對(duì)的圓心角為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)
=2.4/2+24^2/(8*2.4)
=31.2
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((24/2)/31.2)
=45.24度
=45.24*PI/180
=0.789582弧度
C=R*A=31.2*0.789582=24.635