An observer, 1.5 m, tall, is 28.5 m away from a 30 m high tower. Determine the angle of elevation of the top of the tower the eye of the observer.

Given:

Height of observer (say ED) = 1.5 m

Height of tower (say AC) = 30 m

Distance between observer and tower (say CD) = 28.5 m

Angle of elevation (∠AEB) = Ɵ (say)

Clearly,

Perpendicular distance between top of tower and eye of observer AB = AC – CB

⇒ AB = 30 m – 1.5 m

⇒ AB = 28.5 m

And,

BE = CD = 28.5 m

Now,

⇒ tan θ = 1

⇒ θ = 45°

Hence, Angle of elevation = 45°