To find \(\theta\), we use the formula for work done by a force at an angle:

\(\text{Work Done (WD)} = Fd \cos \theta\)

Given: \(F = 20 \text{ N}\), \(d = 1.5 \times 12 \text{ m} = 18 \text{ m}\), and \(\text{WD} = 50 \text{ J}\).

Substitute these values into the formula:

\(50 = 20 \times 18 \times \cos \theta\)

Simplify to find \(\cos \theta\):

\(\cos \theta = \frac{50}{360}\)

\(\cos \theta = 0.1388\)

Find \(\theta\) using the inverse cosine function:

\(\theta = \cos^{-1}(0.1388)\)

\(\theta \approx 82^\circ\)