(i) To find \(F\), use the Pythagorean theorem for the components:

\(F^2 = 27.5^2 + (-24)^2\)

\(F = \sqrt{27.5^2 + 24^2} = 36.5\)

To find \(\alpha\), use the tangent function:

\(\tan \alpha = \frac{-24}{27.5}\)

\(\alpha = \arctan\left(\frac{-24}{27.5}\right) = 41.1^\circ\)

(ii) The second force acts at 90° anticlockwise, so the angle between the forces is \(\alpha + 90^\circ\). The magnitude of the resultant force \(R\) is given by:

\(R = \sqrt{F^2 + 87.6^2 + 2 \cdot F \cdot 87.6 \cdot \cos(90^\circ + \alpha)}\)

\(R = \sqrt{36.5^2 + 87.6^2 + 2 \cdot 36.5 \cdot 87.6 \cdot \cos(90^\circ + 41.1^\circ)} = 94.9\)

To find \(\theta\), use the tangent function:

\(\tan \theta = \frac{87.6 \cdot \sin(48.9^\circ) - 24}{27.5 + 87.6 \cdot \cos(48.9^\circ)}\)

\(\theta = \arctan\left(\frac{87.6 \cdot \sin(48.9^\circ) - 24}{27.5 + 87.6 \cdot \cos(48.9^\circ)}\right) = 26.3^\circ\)