1、12
2、15/4
3、8/9
4、D
5、C
6、2
7、设PB = a,PA = 2a,则AB = 3a,AC = 3a2.
BQ = 32a,BC = 332a,QC = 3a,AQ = 212a,cos∠AQC = 277.
8、∵ ∠ABC = 75°,∠ADB = 30°,
∴ ∠ABD = 45°,
∵ AF ⊥ BC,
∴ ∠FAD = 90°,过A作AM ⊥ BD,垂足为M,在Rt△AMN中,∠ANM = 60°,
∵ DN = 4,
∴ AN = 2.MN = 1.AM = AN,sin60°= 3.在Rt△ABM中,∠BAM = ∠ABM = 45°,
∴ BM = AM = 3.BN = BM - MN = 3 - 1.