2. I assume that you mean with "vertical" the perpendicular direction to the base of 3 m length(?)
3. The two chains ( ) have to hold the dog which pulls with a force . The directions of the chains are determined by the given angles.
4. Calculate the components of using Sine rule:
Calculate similarly. I've got
That means: The two stakes will hold the dog.
5. If the dog pulls directly in the direction of the base (see green arrow!) it will come free of the right stake, then it has to pull in the opposite direction to pull out the second stake.