What is the value of x in the diagram below?

Hi, 
The answer will be  .

Now how is that, there is a rule for the right angled triangle which says:

cosθ =  so, if we applied this rule on the lower triangle we can say: cos30°=  and therefore the hypotenuse =  =  .

now in the upper triangle we will apply the same rule so,
cos45°=
and the adjacent side in the upper triangle is and the hypotenuse is x.
so cos45°= and then we can say 
x= = .