Resolving forces involving an elastic string

[thebosonbreaker]

Homework Statement

A light elastic string of natural length 0.3m has one end fixed to a point on a ceiling. To the other end of the string is attached a particle of mass M. When the particle is hanging in equilibrium, the length of the string is 0.4m.
(a) Determine, in terms of M and g (take g = 9.8 ms^-2), the modulus of elasticity of the string.
(b) A horizontal force is applied to the particle so that it is held in equilibrium with the string making an angle α with the downward vertical. The length of the string is now 0.45m. Find α, to the nearest degree.

Homework Equations

F = ke (Hooke's law)
Modulus of elasticity, λ = kL

The Attempt at a Solution

I have no problem with part (a).
I simply combine the two equations mentioned under "relevant equations" to give:
λ = FL/e = (tension * natural length) / extension = (Mg * 0.3) / 0.1 = 3Mg.

It is part (b) that I'm having trouble understanding.
I have attempted to consider the right-angled triangle formed between the string and the downwards vertical but I don't seem to be getting anywhere.

Could someone please help me by explaining how they would answer part (b)?
Thanks a lot in advance.

 

[Doc Al]

Could someone please help me by explaining how they would answer part (b)?

Consider the forces acting on the particle when the string is at an angle. (One of them will be the tension in the string.) Apply the conditions for equilibrium (for horizontal and vertical forces).