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Heights and Distances — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsHeights and Distances5 Marks
Question
A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height 6m. At a point on the plane, the angle of elevation of the bottom of the flagstaff is 30° and that of the top of the flagstaff is 60°. Find the height of the tower. $\big[\text{Use}\sqrt{3}=1.732\big]$
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Answer


Let AB is the tower of height h meter
In right $\triangle\text{BOA},$
$\frac{\text{OA}}{\text{AB}}=\cot30^\circ$
$\Rightarrow\frac{\text{OA}}{\text{h}}=\sqrt{3}$
$\Rightarrow\text{OA}=\text{h}\sqrt{3}\text{m}\dots(\text{i})$
In right $\triangle\text{COA},$
$\frac{\text{OA}}{\text{AC}}=\cot60^\circ$
$\Rightarrow\frac{\text{OA}}{\text{h}+6}=\frac{1}{\sqrt{3}}$
$\Rightarrow\text{OA}=\frac{\big(\text{h}+6\big)}{\sqrt{3}}\text{m}\dots(\text{ii})$
From (i) and (ii),
$\frac{\big(\text{h}+6\big)}{\sqrt{3}}=\text{h}\sqrt{3}$
$\Rightarrow\text{h}+6=3\text{h}$
$\Rightarrow2\text{h}=6$
$\Rightarrow\text{h}=3$
Hence, the height of the tower is 3m.

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