Answer
See the answer below.
Work Step by Step
From the right angle sketched,
$\sin45^{\circ}=\frac{\text{opposite side}}{\text{hypotenuse}}=\frac{PM}{OP}=\frac{PM}{4}$
$\implies PM=4\sin45^{\circ}$
Similarly, $\cos45^{\circ}=\frac{\text{adjacent side}}{\text{hypotenuse}}=\frac{OM}{OP}=\frac{OM}{4}$
$\implies OM=4\cos45^{\circ}$
