The exercise involves calculating the resultant vector from three given vectors with magnitudes and directions. Here's the step-by-step plan for solving it:

Vectors:

1. Vector 1: Magnitude = $8 \, \text{cm}$, Direction = $45^\circ$
2. Vector 2: Magnitude = $7 \, \text{cm}$, Direction = $15^\circ$ (downward)
3. Vector 3: Magnitude = $3 \, \text{cm}$, Direction = $30^\circ$ (downward)

We will:

1. Resolve each vector into its horizontal ($x$) and vertical ($y$) components.
2. Sum the components for all vectors to get the net $x$- and $y$-components.
3. Calculate the resultant magnitude and direction using these net components.

Would you like me to perform the calculations step-by-step?