题目
已知弓形的弦长为4.3m,7m,怎样计算弓形的周长?
请写出公式及说明,
请写出公式及说明,
提问时间：2021-03-24
答案
已知弓形的弦长为L=4.3m,高H=1.7m,怎样计算弓形的周长?
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)
=1.7/2+4.3^2/(8*1.7)
=2.2096m
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((4.3/2)/2.2096)
=153.33度
弓形的周长=2*PI*R*A/360+L
=2*PI*2.2096*153.33/360+4.3
=10.213m
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)
=1.7/2+4.3^2/(8*1.7)
=2.2096m
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((4.3/2)/2.2096)
=153.33度
弓形的周长=2*PI*R*A/360+L
=2*PI*2.2096*153.33/360+4.3
=10.213m
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