A horizontal beam is subjected to forces. Calculate the tension in the supporting cable and the reaction forces at the pivot.

To solve this problem, we will analyze the forces and torques acting on the horizontal beam, assuming it is in static equilibrium. We will take the left end of the beam as the pivot point for calculating torques. Let $g = 9.8 \, \text{m/s}^2$.

First, let's identify the forces and their components:

1. Force $F_1 = 30 \, \text{N}$: This force is applied at the left end, pointing downwards and to the left. The angle with the horizontal is $30^\circ$.
   • Horizontal component: $F_{1x} = -30 \cos(30^\circ)$ (to the left)
   • Vertical component: $F_{