Question

弦长为4.9米,弓形高为0.7米,求弧长

Answer 1

弦长为L=4.9米,弓形高为H=0.7米,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)

=0.7/2+4.9^2/(8*0.7)

=4.6375米

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

=2*ARC SIN((4.9/2)/4.6375)

=63.78度

C=PI*R*A/180=PI*4.6375*63.78/180=5.162米