已知弦长1500弦高380求弧长
1个回答

答:

弦长AB=1500,弦高CD=380

则半弦长AD=BD=750

设圆半径R,根据勾股定理有:

R^2=AD^2+(R-CD)^2

R^2=AD^2+R^2-2CD*R+CD^2

R=(AD^2+CD^2)/(2CD)

=(AD^2)/(2CD)+CD/2

=750*750/(2*380)+380/2

=930.1315

圆心角2a,则sina=AD/R=750/930.1315=0.8063375

a=0.9379335弧度

所以:弧长=2aR=2*0.9379335*930.1315=1744.8

所以:弧长为1744.8