.Melody,I don't think simply plugging in values is what the question is really about.This is testing one's knowledge of the addition formulae,properties of triangles and manipulation of fractions. As below:

sin(a+b)=sin(a)cos(b) +cos(a)sin(b) so you can write sin70 as

sin(70)=sin(40)cos(30) +cos(30)sin(40)

Now the expression reads

8sin(40)/sin(40)cos(30)+cos(30)sin(40).One should also know (from the equilateral triangle) that cos(30)=1/sqrt2.

So now all we have to do is simplify a fraction,getting

8sin(40)/sin(70)= 8sin(40)/(1/sqrt2sin(40) +1/sqrt2sin(40)

=8sin(40)/(2/sqrt2sin(40)

=8sin(40)/sqrt2sin(40)

Now the sin(40)'s cancel and all you have to do is resolve 8/sqrt2 and the answer is 4 times root 2.