In the figure let AB be the pole and BC is its shadow. Join A and C. We get a right-angled triangle ∆ABC. Angle of elevation of the sun is ∠ACB. Given that, AB = BC. We use trigonometric ratio tan taking AB as height and BC as base to find the angle ∠BCA.

In ∆ABC,

or,

since we know that tanθ is 1 whenever θ = 45°.

So, the correct option is (C).