#### Answer

$sin (45^{\circ}) = \frac{1}{\sqrt{2}}$

#### Work Step by Step

Let's consider a triangle with angles $45^{\circ}, 45^{\circ},$ and $90^{\circ}$ that has sides of length $1, 1,$ and $\sqrt{2}$.
Let $x = 1, y= 1$, and $r = \sqrt{2}$.
Then: $sin(45^{\circ}) = \frac{y}{r} = \frac{1}{\sqrt{2}}$