The angle of elevation of the top of a tower 24 m high from the foot of another tower in the same plane is 60° . The…
CBSE Class 10 Maths PYQ · Applications of Trig · Double Triangle · 3 Marks · March 2023 · Standard
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233 Marks · March 2023 · Standard
The angle of elevation of the top of a tower 24 m high from the foot of another tower in the same plane is $60^\circ$. The angle of elevation of the top of second tower from the foot of the first tower is $30^\circ$. Find the distance between two towers and the height of the other tower. Also, find the length of the wire attached to the tops of both the towers.
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1 mark for correct figure Let $AB$ and $CD$ be the given towers. $\tan 30^\circ = \frac{h}{x} \Rightarrow x = h\sqrt{3}$ (i) $\tan 60^\circ = \sqrt{3} = \frac{24}{x} \Rightarrow x = \frac{24}{\sqrt{3}}$ or $8\sqrt{3}$ (ii) using (i) and (ii) $x=8\sqrt{3}$ and $h=8$ length of wire = $\sqrt{BE^2 + X^2} = \sqrt{256 + 192} = \sqrt{448}$ m = $8\sqrt{7}$ m
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