What is the equations for tension?

Question

An A-Shapped Ladder, both sides of the ladder are equal in length. The ladder is standing on a frictionless horixontal surgace, and only the crossbar )which has a negligible mass) of the "A" keeps the ladder from collapsing. The ladder is uniform and has a mass of 20.0 kg. The angle the ladder makes is 30.0 degrees. The length of the ladder if 4.00 m.

Answer 1

(tension in crossbar) * (its height) =(half of ladder weight) * (length of ladder * sin(30/2) / 2)

Answer 2

Here goes

let F = the mass of the ladder, acting vertically downwards

then F/2 = the vertical reaction forces at each leg acting upwards

Now, the tension, X, in the cross member is equal to the horizontal component of the vertical reaction force at each leg, or:

tan(30) = F/2X
or X = F/ [2*tan(30)]
X= [20kg * 9.81 m/s^2] / [2*tan(30)]
X = 196.2 / 1.1547 kgm/s^2
X = 170 N