What is the value of in the diagram?

As follows:

Can you take it from here?

need more help.

That straight up and down line, let's just call that A, as in altitude. Use trig. 

so, in a right triangle. sine of an angle is opposite over hypotenuse 

                                                      sine 60^o  =  A/2   

                                                      0.866      =  A/2  

                                                                 A  =  1.732      

now that you know A, go to the triangle on the other side. 

                                                       sine 45^o  =  1.732/x 

                                                       0.707      =  1.732/x

                                                                   x  =  1.732/0.707 

                                                                   x  =  2.45  

_.

Using law of sines

2/ sin45 = x/sin60

sin60 * 2/sin45 = x

sqrt3 / (sqrt2/2) = x

x = 2 sqrt3 / sqrt2       =  ~ 2.4494897