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°.
Find the height of the chimney. [CBSE 2013C]

Answer 1

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

We have,
$$\begin{gathered} \mathrm{BD}=\mathrm{CE}=1.5\mathrm{m},\mathrm{BC}=\mathrm{DE}=30\mathrm{m}\mathrm{and}\angle \mathrm{ACB}=60° \\ \mathrm{In}∆\mathrm{ABC}, \\ \tan 60°=\frac{\mathrm{AB}}{\mathrm{BC}} \\ \Rightarrow \sqrt{3}=\frac{\mathrm{AD}-\mathrm{BD}}{30} \\ \Rightarrow \mathrm{AD}-1.5=30\sqrt{3} \\ \Rightarrow \mathrm{AD}=30\sqrt{3}+1.5 \\ \Rightarrow \mathrm{AD}=30\times 1.732+1.5 \\ \Rightarrow \mathrm{AD}=51.96+1.5 \\ \Rightarrow \mathrm{AD}=53.46\mathrm{m} \end{gathered}$$

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