1. At first let us find the value of angle UXW:

using the sin theorem we obtain the following equation:

YZ / sin(UXW) = XY / sin(90 - UXW) = XY / cos(UXW)

-> UXW = arctan(0.5) ~ 26.565

2. now let us apply the sin theorem to triangle XYU (I'll define UY & VY as L)

L / sin(UXW) = XY / sin(XUY)

3. we apply the sin theorem again only this time in triangle VYW:

L / sin(90) = VW / sin (VYW)

4. the angle VYW can be easily obtained if we observe that angle YZU equals 116.565, ang(ZYU) = 63.435-sin(XUY) -> ang(VYW) = sin(XUY + 6.565)

thus we obtain two equations in two unknows namely (ang(XUY) and L):

I. L/sin(26.565) = 200 / sin(XUY)

II. L = 400 / sin(XUY + 6.565) = 400 / [sin(XUY)cos(6.565) + sin(6.565)cos(XUY)]

(WY can be easily obtained using the pythagorean theorem after you'll find L)

I think that u'll be able to do the rest...