Question

An observer 1.5m tall is 30 away from a chimney. The angle of elevation of the top of the chimney from his eye is 60°. Find the height of the chimney.

Answer 1

Let CE and AD be the heights of the observer and the chimney, respectively.

We have,

BD = CE = 1.5 m, BC = DE = 30 m and ∠ACB = 60°

In △ABC

tan 60° = \(\frac{AB}{BC}\)

\(\Rightarrow\) \(\sqrt{3}=\frac{AD-BD}{30}\)

\(\Rightarrow\) AD - 1.5 = \(30\sqrt{3}\)

\(\Rightarrow\) AD = \(30\sqrt{3}\) + 1.5

\(\Rightarrow\) AD = 30 x 1.732 + 1.5

\(\Rightarrow\) AD = 51.96 + 1.5

\(\Rightarrow\) AD = 53.46 m

So, the height of the chimney is 53.46 m (approx).