Let the height of the tower be h.
The shadow length is 31×h=3h.
The tower, its shadow, and the line from the sun form a right-angled triangle where:
- Height of tower (perpendicular) = h
- Shadow length (base) = 3h
- Angle of elevation = θ
Using the tangent ratio:
tanθ=ShadowHeight
tanθ=3hh
tanθ=h×h3
tanθ=3
From standard trigonometric values, tan60°=3.
Therefore, θ=60°.