Question

已知弦长9,求弧长 求比较容易明白的解释方式.

Answer 1

已知弦长L=9,弦高H=2,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)

=2/2+9^2/(8*2)

=6.0625

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

=2*ARC SIN((9/2)/6.0625)

=95.85度

=95.85*PI/180

=1.6729弧度

C=A*R=1.6729*6.0625=10.142