The work done by the tension in the rope is given by the formula:

\(\text{Work Done (WD)} = F \cdot d \cdot \cos \alpha\)

where \(F\) is the force (tension), \(d\) is the distance, and \(\alpha\) is the angle of inclination.

Substituting the given values:

\(8200 = 180 \times 50 \times \cos \alpha\)

Simplifying, we get:

\(8200 = 9000 \cos \alpha\)

\(\cos \alpha = \frac{8200}{9000}\)

\(\cos \alpha = 0.9111\)

Taking the inverse cosine, we find:

\(\alpha = \cos^{-1}(0.9111)\)

\(\alpha \approx 24.3^\circ\)