# It is found that on walking x metres towards a chimney in a horizontal line through its base, the elevation of its top changes from 30° to 60° . The height of the chimney is

A. $3 \sqrt{2} x$ B. $2 \sqrt{3} x$ C. $\frac{\sqrt{3}}{2} x$ D. $\frac{2}{\sqrt{3}} x$ Answer: Option C
Here AB is the chimney of height h By walking x meters toward chimney the angle of elevation changes from 30° to 60° In Δ ABH, $\begin{array}{l}\tan60^{\circ}=\frac{\text{h}}{\text{y}}\\ \mathrm{h}=\sqrt{3}\mathrm{y}\\ \frac{\mathrm{h}}{\sqrt{3}}=\mathrm{y}\ldots\ldots\left(i\right)\\ \text{ In }\triangle\text{ ABG }\\ \tan30^{\circ}=\frac{\mathrm{h}}{\mathrm{x}+\mathrm{y}}\\ \frac{1}{\sqrt{3}}=\frac{\mathrm{h}}{\mathrm{x}+\mathrm{y}}\\ \sqrt{3}\mathrm{\text{h}}=\mathrm{x}+\mathrm{y}\\ \sqrt{3}\mathrm{\text{h}}-\frac{\mathrm{h}}{\sqrt{3}}=\mathrm{x}\ ..(\text{from eqn-i})\\ \frac{2\mathrm{~h}}{\sqrt{3}}=\mathrm{x}\\ \mathrm{h}=\frac{\sqrt{3}\mathrm{x}}{2}\end{array}$