Question

Find the angle of elevation when length of shadow of tower is equal to height of tower

Answer 1

Given,
The length of the shadow is equal to the height of the tower.

Here, In ∆ABC (right angled at B)
Let, AB be height of the tower
CB be length of the shadow
Also, Angle of elevation, ACB be θ

We have,
AB=CB=x

Now,
tanθ=AB/CB
or tanθ=x/x
or tanθ=1
or tanθ=tan45° (tan45°=1)
or θ=45°

Therefore, The angle of elevation is 45°.