MATH PROBLEM pls help me!!!?

Question

any one know how to do either of these prob?? thank you...

2. the triangle ABC has an obtuse angle at B, BC= 10.2, A=x and B=2x. (the A and B have a little curved line over them)
a) find AC in terms of cos x
b) given that the area of triangle ABC is 52.02 cos x, find angle C. ( the C has a curved line over it)

3. The position vectors of points P and Q are {2, -3, 1} and {2, 2, -4 } respectively. the origin is at O. find...
a) the angle POQ
b) the area of the triangle OPQ

please help. thanks

Answer 1

Problem#2.
a) Using Sine Law, and the fact B = 2A, we have:
BC/Sin (A) = AC/Sin (B), or
10.2/ Sin (x) = AC/ Sin (2x) = AC/ [2Sin (x) Cos (x)]
Therefore, AC = 20.4Cos (x)
b) 52.02 Cos (x) = BC*AC*Sin (C)/2 = (10.2)^2 Sin(C)Cos(x)
Hence C = Arc sin (52.02/ (10.2)^2)

Problem#3.
a) Using Dot Product of the vectors:
OP.OQ = 2*2 - 2*3 - 4*1 = -6
= |OP|*|OQ|*Cos(POQ) = sqrt(14)* 2sqrt(6) Cos (POQ)
= 4sqrt(21) Cos(POQ)
Hence POQ = Arc cos (-3/(2sqrt(21)))
b) Use formula: Area = |OP|*|OQ|* Sin (POQ)/2