MathDB

12

Part of 1995 AIME Problems

Problems(1)

Square Pyramid

Source:

12/22/2005
Pyramid OABCDOABCD has square base ABCD,ABCD, congruent edges OA‾,OB‾,OC‾,\overline{OA}, \overline{OB}, \overline{OC}, and OD‾,\overline{OD}, and ∠AOB=45∘.\angle AOB=45^\circ. Let θ\theta be the measure of the dihedral angle formed by faces OABOAB and OBC.OBC. Given that cos⁡θ=m+n,\cos \theta=m+\sqrt{n}, where mm and nn are integers, find m+n.m+n.
geometry3D geometrypyramidtrigonometryanalytic geometryAIMEgeometry solved