Block on Incline

When we resolve weight and applied force perpendicular to the plane we get normal reaction:

$N = mg(\sin\theta + \cos\theta)$

For finding the value of $\theta$ for which $N$ is maximum, we use calculus. Differentiating $N$ with respect to $\theta$ , we get:

$\frac{dN}{d\theta} = mg(\cos\theta - \sin\theta)$

Equating this to $0$ , we get: $\theta_{max} = 45$ degrees

The maximum reaction of plane to horizontal force can only be achieved with 45 degree incline plane. A physics fact.