Question

When the top of the chimney of a factory is seen from a point on the roof of a three-storied building of $9\sqrt{3}$ metre height, the angle of elevation is ${30}^{\circ }$. If the distance between the factory and chimney is 30 metres, calculate the height of the chimney.

• A. $17\sqrt{3}$ m
• B. $19\sqrt{3}$ m
• C. 25 m
• D. $7(\sqrt{3}+1)$

Answer 1

The correct option is B

$19\sqrt{3}$ m

Let AB be the chimney and CD be the building.

From the figure, CE = BD

From $△AEC,tan{30}^{\circ }=\frac{AE}{CE}$

$\Rightarrow \frac{1}{\sqrt{3}}=\frac{AE}{CE}$

$\Rightarrow \sqrt{3}AE=CE$

$\Rightarrow \sqrt{3}AE=BD$

$\Rightarrow \sqrt{3}AE=30$

$\Rightarrow AE=10\sqrt{3}$

$\Rightarrow AB=AE+BE$

$\Rightarrow AB=10\sqrt{3}+9\sqrt{3}$

$\Rightarrow AB=19\sqrt{3}$