Calculating tension in a wire holding beam against wall

[mashedpotato]

Hi, this is my first forum post - sorry if I'm in the wrong place, or I've done something wrong!

Homework Statement

Here goes: There is a beam of 0.5m length hinged to a wall at a right angle with 200N mass at the end of the beam. This is supported by a wire T at angle 30°. The question asks to find tension in T.
It seems I can answer the question correctly, however, looking at the solutions, I do not understand why an answer was obtained in such a way...

Homework Equations

Turning Moment = force x distance.

The Attempt at a Solution

Ok, so I made the triangle into a trigonometry problem. Opposite = wall, Adjacent = beam and Hypotenuse = Wire / Tension.
Opp = 200N, I want to find Hyp ∴ Hyp = 200 / sin(30) = 400N. This answer is actually correct, but the answers use this as a solution:
T sin(30) x 0.5 = 200 x 0.5

If someone could please help, I would be extremely grateful, as this question has been frustrating me for some time.
mashedpotato.

 

[mashedpotato]

Ok, sorry for this post but I *think* I've found the solution. Please do correct me if I'm wrong.

So, technically:
Hyp (T or Tension) = 200 / sin(30)
sin(30) * T = 200

But the answer uses: T sin(30) * 0.5 = 200 * 0.5 which is the same as saying sin(30) * T = 200

Thanks & Best Regards,
mashedpotato

 

[haruspex]

But the answer uses: T sin(30) * 0.5 = 200 * 0.5

That solution is taking moments about the hinge where the beam meets the wall, whereas your method looked at vertical components of forces.
Your method is unsafe because you have effectively assumed there is no vertical force from the hinge. That happens to be true in this case, but if you move the point of attachment of wire to beam to somewhere else along the beam it will not be, and the book method succeeds while yours fails.