Question

弦长6M,弧高0.6M,求弧长?M

Answer 1

弦长L=6M,弧高H=0.6M,求弧长C?

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*R*H+H^2+L^2/4

2*R*H=H^2+L^2/4

R=H/2+L^2/(8*H)

=0.6/2+6^2/(8*0.6)

=7.8米

A=2*ARC SIN((L/2)/R)

=2*ARC SIN((6/2)/7.8)

=45.24度

C=PI*R*A/180=PI*7.8*45.24/180=6.1587米