一个扇形,弦长L=2.8米,拱高H=0.415米,求弧长C是多少?
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)
=0.415/2+2.8^2/(8*0.415)
=2.569米
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((2.8/2)/2.569)
=66.045度
=66.045*PI/180
=1.152708弧度
C=R*A=2.569*1.152708=2.961米