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Height and Distances — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsHeight and Distances5 Marks
Question
A $20 \ m$ high vertical pole and a vertical tower are on the same level ground in such a way that the angle of elevation of the top of the tower, as seen from the foot of the pole is $60^\circ$ and the angle of elevation of the top of the pole, as seen from the foot of the tower is $30^\circ$ . Find:
$(i)$ the height of the tower ;
$(ii)$ the horizontal distance between the pole and the tower.
✓

Answer


Let $AB$ be the tower and $CD$ be the pole .
Given $, CD= 20m,\angle ADB = 60^\circ$ and $\angle CBD= 30^\circ$
In $\triangle BDC,$
$\frac{C D}{B D}=\tan 30^{\circ}$
$\Rightarrow B D=20 \text { sqrt } 3\ m$
$\ln \triangle D B A,$
$\frac{A B}{B D}=\tan 60^{\circ}=\sqrt{3}$
$\Rightarrow A B=20 \text { sqrt } 3 x \times \operatorname{sqrt} 3=60\ m $
Hence ,
$(1)$ Height of the tower $= 60\ m$
$(2)$ horizontel distan ce between the pole and tower
$=20 \times 1.732=34.64\ m$

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