Find the angle of elevation of the sun (sun’s altitude) when the length of the shadow of a vertical pole is equal to its height.

Let the position of the sun be at O and AB be the height of the pole.

Now BC is the shadow cast by the pole. From point C, the angle of elevation of the top of the pole (point A) and the sun would be the same.

Since length of shadow is equal to the height of the vertical pole.

Therefore AB = BC

In ∆ABD

tan θ =

tan θ = ⇒ 1

θ = tan 1 (since tan 45°= 1)

θ = 45°

Therefore angle of elevation is 45°