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Height and Distances — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsHeight and Distances5 Marks
Question
A vertical pole and a vertical tower are on the same level ground in such a way that from the top of the pole, the angle of elevation of the top of the tower is $60^\circ$ and the angle of depression of the bottom of the tower is $30^\circ.$ Find: the height of the tower, if the height of the pole is $20\ m.$
✓

Answer


Let $AB$ be the tower and $CD$ be the pole.
Then $\angle ACE=60^\circ$ and $\angle BCE=30^\circ$
In $\triangle BEC,$
$\frac{B E}{E C}=\tan 30^{\circ}$
$\Rightarrow \frac{20}{E C}=\frac{1}{\sqrt{3}}$
$\Rightarrow E C=20 \sqrt{3}\ m$
In $\triangle AEC,$
$\frac{A E}{E C}=\tan 60^{\circ}$
$\Rightarrow A E=20 \sqrt{3} \times \sqrt{3}=60\ m$
$\therefore$ Height of the tower $=A B=A E+E B$
$=(60+20)=80\ m $

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