Question

A uniform horizontal beam with a length of 8m and a weight of 200N is attached to a wall by a pin connection. Its far end is supported by a cable that makes an angle of 53° with the beam (Figure below). If a 600N person stands 2m from the wall, find the tension in the cable as well as the magnitude and direction of the force exerted by the wall on the beam.

Answer 1

first, the diagram.
T is tension.
fup is the force on the pin holding it upwards
fout is the force on the pin pushing it outwards.
vertica forces = zero
Fup-6000-2000+Tsin53=0
horizontal forces =zero
Fout-Tcos53=0
sum moments about pin is zero.
-6000*2-2000*4+Tsin53=zero

so you have three indep equations, three unknowns. For the force by the wall on the beam, combine Fup and Fout into a composite vector.