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The angle of elevation of the top of a tower 30 m high from the foot of another tower in the same plane is 60°. The angle of elevation of the top of second tower from the foot of the first tower is 30°. 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.

Posted by Utkarsh Kumar Yadav 2 years ago

CBSE > Class 10 > Mathematics

5 answers

Preeti Dabral 2 years ago

Let distance between the two towers = AB = x m
and height of the other tower = PA = h m
Given that, height of the tower = QB = 30 m and $\angle$ QAB = 60°, $\angle$ PBA = 30°.

Now, in $\Delta Q A B, \tan 60^{\circ}=\frac{Q B}{A B}=\frac{30}{x}$
$\Rightarrow \sqrt{3}=\frac{30}{x}$
$x=\frac{x^{2}}{3}-\frac{x}{3}-\frac{x-3}{3}-x+0.5 \pi$
and in $\Delta P B A$
$\tan 30^{\circ}=\frac{P A}{A B}=\frac{h}{x}$
$\Rightarrow \frac{1}{\sqrt{3}}=\frac{h}{10 \sqrt{3}}$ $[\because x=10 \sqrt{3} \mathrm{m}]$
$\Rightarrow h = 10 m$
Hence, the requied distance and height are $10\sqrt3$ and 10m, respectively.

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Ankit Class 2 years ago

Ye figure draw kaise ki ho batao

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Ankit Class 2 years ago

PQ is the length of the wire attached to the tops of both the towers

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Ankit Class 2 years ago

PQ=√x^2 +(30-h)^2 . PQ=√(10√3)^2 + (30-10)^2 . PQ=√ 300+400. PQ=√700. PQ= 10√7 m

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Ankit Class 2 years ago

Math standard mein ye question puchha tha n mere mein bhi puchha tha set 1 tha mera 21 feb ko paper tha n

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CBSE > Class 10 > Mathematics