Question 287719
Let's use x instead of theta.

We have sin(x) = sqrt(2)/2

The right triangle formed by x is "similar" to one with side sqrt(2) and hypotenuse 2.

If the unknown side is y, by the Pythagorean Theorem we have:

y^2 + sqrt(2)^2 = 2^2
y^2 + 2 = 4
y^2 = 2
y = sqrt(2)

The triangle is isoceles.

Now we have the two sides = sqrt(2)) and the hypotenuse = 2, so we can calculate any of the trig functions of the angle. For example, the tangent is sqrt(2)/sqrt(2) = 1.