What is the value of y?

enter your answer, as an exact value, in the box.

We know the bottom triangle is a 45, 45, 90 triangle, so the hypotenuse is √2 times the value of the legs:

(√2)(√2)
=√4
=2

Now, we can use this to solve for y. The top triangle is a 30, 60, 90 triangle. The side we found above is the side across from the 30 degree angle. The side opposite the 60 degree angle is √3 times the side across the 30 degree angle. Therefore, we can solve for y by multiplying 2 by √3

y=2√3