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Verified Answer :

The triangle is a 30-60-90 triangle.
x=\(16\)
y=\(16 \sqrt{3}\)

Just to add, I think you mixed up the hypotenuse and opposite side. 32 is the hypotenuse because it is opposite the right angle, and y is the opposite side. 

To find side x, we have an angle, the hypotenuse, and the adjacent side. So we would cos(x)=adjacent/hypotenuse.
cos(60)=x/32 (cross multiply)
32cos(60)=x
32
(1/2)=x
x=16

Then to find y, we have an angle, the hypotenuse, and the opposite side. So we would use sin(x)=opposite/hypotenuse
sin(60)=y/32 (cross multiply)
32sin(60)=y
y=32
√3/2
y=16√3

Hope this helps :)