Question

将正方形ABCD沿着对角线BD折成一个四面体ABCD,在下列给出的四个角度中,

Answer 1

选③90° ④120°

根据余弦定理得:

设AC,BD的交点是O,∠ACO=m,正方形的边长是1

∵AO^2=AC^2+OC^2-2AC×OCcosm

∴cosm=(AC^2+OC^2-AO^2)/2(AC×OC)

∴cosm=[AC^2+(√2/2)^2-(√2/2)^2]/(AC√2)

=AC^2/(AC√2)

=AC/√2

∵0＜AC＜√2

∴0＜AC/√2＜1

∴0＜cosm＜1

∴0°＜m＜90°