Problem:
In the adjoining figure of a rectangular solid, ∠DHG=45∘ and ∠FHB=60∘. Find the cosine of ∠BHD.
Answer Choices:
A. 63
B. 62
C. 36
D. 46
E. 46−2
Solution:
Without loss of generality, let HF=1 in the adjoining figure. Then BH=2,
BF=3=DG=GH, and DH=6
Since DC=HC=3,△DCB≅△HCB and DB=HB=2. Since △DBH is isoceles,
cosθ=2216=46