Make a drawing. Label a triangle in quadrant $1$ with the information given in the problem.
Notice that you are given the horizontal distance and you know the radius (hypotenuse).

$\cos (\theta) = \frac{53}{100}. \text{ Solve for } \theta .$

Consider where she would be if she were in one of the other three quadrants with the same reference angle.

$58^{\circ},122^{\circ},238^{\circ}\text{ or}\ 302^{\circ}$