Answer
Red Riding Hood pulls at an angle of $13.0^{\circ}$ with respect to the vertical.
Work Step by Step
Before Red Riding Hood starts pulling, the only horizontal force on the basket is the horizontal component of the wolf's force. Since the net force is directed straight up, the horizontal component of Red Riding Hood's force must be equal in magnitude to the horizontal component of the wolf's force.
We can find the angle $\theta$ with respect to vertical at which Red Riding Hood pulls:
$(12~N)~sin(\theta) = (6.4~N)~sin(25^{\circ})$
$sin(\theta) = \frac{(6.4~N)~sin(25^{\circ})}{12~N}$
$sin(\theta) = 0.2254$
$\theta = arcsin(0.2254)$
$\theta = 13.0^{\circ}$
Red Riding Hood pulls at an angle of $13.0^{\circ}$ with respect to the vertical.
