Ladder on the Wall

The diagram above indicates the forces acting on the system while in stasis. The point B is the midpoint between points A and C. In the following equations above, $M_B$ indicates moment about point B. Let the length of the rod be $L$

$\sum F_{horizontal} = 0 \implies \mu N_1 - N_2 = 0$ $\sum F_{vertical} = 0 \implies \mu N_2 + N_1 = W$ $\sum M_B = 0 \implies \left(N_2\cos{\theta} +\mu N_2\sin{\theta}\right) \frac{L}{2}=\left(N_1\sin{\theta} -\mu N_1\cos{\theta}\right) \frac{L}{2} \implies \frac{N_2}{N_1} = \tan\left(\theta - \arctan(\mu)\right)$

So three equations with three unknowns $N_1$ , $N_2$ and $\theta$ can be easily solved giving the answer as:

$\boxed{\theta = 2\arctan(\mu)}$

Note: $\arctan[.]$ is the inverse tangent function.