It is best to apply vector method to this kind of problem, and the geometric method is as follows:
Analysis: in the V-ABCD of the ∵ quadrangular cone, VA⊥ ABCD (square), VA=AB, and M is the midpoint of VA.
∴ surface VAB⊥ surface ABCD, two surfaces intersect AB.
∵ABCD is a square.
∴BC⊥ Ground Assembly Building
∵BC∈∴ Facing MBC, MBC⊥ Facing VAB, two faces meet BM.
Take BC midpoint n, VB midpoint o
Like OP⊥BM
∴OP⊥ Facing MBC
Connect, PN
∴ON//VC, PN is the projection of MBC on the plane.
∴∠ONP is the angle formed by a straight line VC and a plane MBC.
VA = AB = 2
∴vc=√(va^2+ab^2+bc^2)=2√3==>； On =√3
∠VBA=∠VBM+∠MBA=45
∵M is the midpoint of VA == >; tan∠MBA= 1/2
tan∠VBA=tan(∠VBM+∠MBA)=tan45
(tan∠VBM+tan∠MBA)/( 1-tan∠VBM * tan∠MBA)= tan 45
(Tan ∠ VBM+1/2)/(1-1/2 Tan ∠VBM)= 1
tan∠VBM = 1/3 = = & gt； sin∠VBM=√ 10/ 10
VB=2√2== >OB=√2
∴OP=OB*sin∠VBM=√20/ 10
∴sin∠onp=(√20/ 10)/√3=√ 15/ 15