已知弦长180,求圆心角度.已知圆心角度41.25,弦长31.75,求拱高.已知圆心角度41.25,拱高5,求弦长.

Question

已知弦长180,求圆心角度.
已知圆心角度41.25,弦长31.75,求拱高.
已知圆心角度41.25,拱高5,求弦长.

Answer 1

已知弦长L=180,拱高H=29.求圆心角度A?
弧半径为R.
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)
=29/2+180^2/(8*29)
=154.155
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((180/2)/154.155)
=71.44度

已知圆心角度A=41.25,弦长L=31.75,求拱高H?
弧半径为R.
R=(L/2)/SIN(A/2)
=(31.75/2)/SIN(41.25/2)
=45.067
H=R-R*COS(A/2)
=45.067-45.067*COS(41.25/2)
=2.889

已知圆心角度A=41.25,拱高H=5,求弦长L?
弧半径为R.
COS(A/2)=(R-H)/R
COS(41.25/2)=(R-5)/R
0.935906=(R-5)/R
R-0.935906*R=5
R=78.01
L=2*R*SIN(A/2)
=2*78.01*SIN(41.25/2)
=54.958