Solve the Problem $P O Q$ Be Designated $\theta$ Angles $P Q R$

Multiple Choice

Solve the problem.
-Let angle $P O Q$ be designated $\theta$ . Angles $P Q R$ and VRQ are right angles. If $\theta = 45 ^ { \circ }$ , find the exact length of OU.

A) 1
B) $\frac { \sqrt { 2 } } { 2 }$
C) $\sqrt { 2 }$
D) 0