Question

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

Answer 1

Given the height of the observer be DE = 1.5 m
That is AB = 1.5 m
Let BC = h is height of the chimney
Hence AC = (h – 1.5) m
Given distance between the observer and the chimney is AD = BE = 28.5 m
In right DCAD, θ = 45°

$tan45=\frac{AC}{AD}$

=> $1=\frac{h-1.5}{28.5}$

=> $h-1.5=28.5$
∴ h = 28.5 +1.5 = 30 m
Thus the height of the chimney is 30 m.