圆弧求弧长!弦长14.1m,5m,求弧长..希望高手给出具体的过程,运算过程也写清楚!不要简洁的答案.

Question

圆弧求弧长!
弦长14.1m,5m,求弧长..
希望高手给出具体的过程,运算过程也写清楚!不要简洁的答案.

Answer 1

弦长L=14.1m,弦高H=1.5m,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)
=1.5/2+14.1^2/(8*1.5)
=17.3175m
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((14.1/2)/17.3175)
=48.05度
=48.05*PI/180
=0.83856弧度
C=A*R
=0.83856*17.3175
=14.522m