Question

what will be angle of elevation of sun when length of shadow of a vertical pole is equal to its height

Answer 1

In right angle ΔABC, AB represents the vertical pole and BC represents the shadow on the ground.θ represents angle of elevation the sun.
tan θ = h / x
But length of shadow = height of the tower, i.e. h = x.
tan θ = h/ h = 1
tan θ = tan 45°
θ = 45°
Thus, angle of elevation of the sun = 45°.

Answer 2

$ab = bc \: \: \: {height = shadow}\\ therefore \: \\ \tan(theta) = \frac{ab}{bc} = 1 \\ theta = 45 \: degree$
hope it helps.