发布时间:2019-07-31 09:55:08
.如图,一个凸八边形ABCDEFGH的八个内角都是135°,连续六边的长依次为AB=7,BC=4,
CD=2,DE=5,EF=6,FG=2.求八边形的边长GH和HA.
ED、CB、GF、HA与水平夹角都是 180 - 135 = 45°;
E向AB作垂线,垂足为 P,则EP = ED/√2 + BC/√2 + CD = 9/√2 + 2;
C向HG作垂线,垂足为 Q,则CQ = ED/√2 + GF/√2 + FE = 7/√2 + 6;
HA/√2 = CQ - CB/√2 - AB = 7/√2 + 6 - 4/√2 - 7 = 3/√2 - 1,HA = 3 - √2;
GH = EP - FG/√2 - HA/√2 = 9/√2 + 2 - 2/√2 - 3/√2 + 1 = 4/√2 + 3;
答:GH = 4/√2 + 3;HA = 3 - √2 。