(i) Using the cosine rule in the triangle formed by the forces:

\(X = 14 - 13 \cos \theta\)

\(Y = 13 \sin \theta\)

\(14^2 + 13^2 - 2 \times 13 \times 14 \cos \theta = 15^2\)

Solving for \(\theta\), we find \(\theta = 67.4^\circ\).

(ii) The component of the resultant in the direction of the 14 N force is:

\(X = 15 \cos \left( \arctan \left( \frac{Y}{X} \right) \right)\)

The component is 9 N.