Answer
$90$ miles north, $120$ miles east
Work Step by Step
The trigonometric ratios are as follows: $\sin \theta= \dfrac{opposite}{hypotenuse}$ ; $\cos \theta= \dfrac{Adjacent}{hypotenuse}$ and $\tan \theta= \dfrac{Opposite}{Adjacent}$
We can use the sine and cosine of the triangle to solve for the distance.
Since, $\cos \theta= \dfrac{Adjacent}{hypotenuse}$
Now, miles to north $ = 150 \times \cos 53^{\circ}=90$ miles
and $\sin \theta= \dfrac{opposite}{hypotenuse}$
Now, miles to east $ = 150 \times \sin 53^{\circ}=120$ miles
