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  • The angle of elevation of the top of a tower is 30degree. If the height of the tower is doubled, then the angle of elevation of its top will also be doubled.

The angle of elevation of the top of a tower is 30°. If the height of the tower is doubled, then the angle of elevation of its top will also be doubled.

Answers (1)

According to question

Case: 1
Here BC is the tower.
Let the height of the tower be H and distance AB = a
In  \bigtriangleupABC
 \tan\theta=\frac{Perpendicular}{Base}

\tan 30^{\circ}= \frac{H}{a}           \left ( \because \theta = 30^{\circ} \right )      

\frac{1}{\sqrt{3}}= \frac{H}{a}\; \cdots \left ( 1 \right )       \left ( \because \tan 30^{\circ} = \frac{1}{\sqrt{3}}\right )                    

Case:2    When height is doubled

Here ED = a
In \bigtriangleup DEF
\tan \theta = \frac{2H}{a}
\tan \theta = \frac{2}{3}   (from (1))
But \tan 60^{\circ}= \sqrt{3}         (If the angle is double)
\sqrt{3}\neq \frac{2}{\sqrt{3}}
Hence the given statement is false.                 

Posted by

infoexpert27

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