Question

An observer 1.5 m tall is 30 m away from a chimney. The angle of elevation of the top of the chimney from his eye is ${60}^{\circ }$. Find the height of the chimney.

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 the distance between the observer and the chimney is AD = BE = 30 m

In right $△CAD,\theta ={60}^{\circ }tan60=\frac{h-1.5}{30}\sqrt{3}=\frac{h-1.5}{30}h-1.5=30\sqrt{3}\therefore h=30\sqrt{3}+1.551.96+1.5=53.46m$

The height of the chimney = 53.46 m