They give us a few of the rare angles we can get exact answers for and then they ask for an approximation. Amateurs.
In the 30/60/90 triangle the sides are in ratio 1:√3:2. So for the big side 22 the altitude h=11 and the part of the base to the right of the right angle is 11√3.
In the 45/45/90 triangle the sides are in ratio 1:1:√2 so the altitude h=x/√2 and the base to the left of the right angle is also h. So
x = h√2 = 11√2
y = 11√3 + 11
I hate ruining a nice exact answer with an approximation but they asked:
Answer: x=15.56 y=30.05
