弦长1.5米,拱高0.3米,求弧长?
问题描述：
弦长1.5米,拱高0.3米,求弧长?
答
弦长L=1.5米,拱高H=0.3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)
=0.3/2+1.5^2/(8*0.3)
=1.0875米
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((1.5/2)/1.0875)
=87.21度
=87.21*PI/180
=1.52203弧度
C=A*R
=1.52203*1.0875
=1.655米