Question

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

Answer 1

Hey there !

Thanks for the question !

Here's the answer !

Refer to the attachment for the diagram

So let the pole be denoted by 'h' and the shadow be denoted by 'x'.

So θ is the angle made by the sun with respect to the tip of the shadow.

We know that Tan θ = Opposite Side / Adjacent Side

In this case, Opposite Side = h and Adjacent Side = x

We are also given that both the shadow and the height of tower are same.

=> h = x

So Tan θ = h / x

=> Tan θ = h / h = 1

We know that Tan 45 = 1. So If Tan θ = 1, then θ must be 45°.

Hence the angle of elevation made by the sun is 45°.

Hope my answer helped !