Objects in equilibrium hinged platform with cable problem

[BrainMan]

Homework Statement

A hinged platform flagpole weighing 500 Newtons is supported in the horizontal position by a cable as shown in figure 4.35

. Find the tension in the cable and the horizontal and vertical forces at the hinge. Angle ø = 30°

Homework Equations

∑F=0
∑T=0
T= F* the lever arm

The Attempt at a Solution

What I did was created the three equations R cos θ -T cos 30=0 for the X forces
where R is the resultant force of the wall acting on the hinge of the beam and T is the tension in the wire. The equation for the Y forces was R sin θ + T sin θ -500=0. Then I made the equation T sin 30 (x) -500 (1/2)(x)=0 for the sum of the torques is zero. My problem is I have four unknowns and only three equations meaning I can't substitute. What do I do now? The correct answer is T = 500 N and Rx= 433 N Ry= 250 N

 

[paisiello2]

Maybe just go ahead and solve for R and T in terms of x and theta and see what happens.

 

[BrainMan]

I don't think that will work because you have more unknowns than you have equations to work with. I tried it and it doesn't seem to work.

 

[paisiello2]

if you did it correctly then I think you would see that one of those variables actually drops out

 

[BrainMan]

Ok I see it now thanks!