Write 'True' or 'False' and justify your answer in each of the following:The angle of elevation of the top of a tower is $30^{\circ}$. If the height of the tower is doubled, then the angle of elevation of its top will also be doubled.

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Given:

The angle of elevation of the top of a tower is $30^{\circ}$. If the height of the tower is doubled, then the angle of elevation of its top will also be doubled.

To do:

We have to find whether the given statement is true or false.

Solution:

The given angle of elevation $=30^o$.

Let the height of the tower$=h$, and the viewer be at a distance of $x$ from the foot of the tower.

Then,

$\frac{h}{x}=tan30^o=\frac{1}{3}\ ........\ ( i)$

If the height of the tower is doubled then the new height $=2h$.

Let the angle of elevation of the top be $\theta$.

Then, $tan\theta =\frac{2h}{x}=2\times \frac{1}{3}=\frac{2}{3}\ ........( ii)$

But if the angle of elevation doubles then it should be $=\theta =2\times 30^o=60^o$.

Then, $tan\theta =tan60^o=3\ ........\ ( iii)$.

Comparing $( ii)$ & $( iii)$, there is a contradiction.

Thus, we came to know, if the height of the tower is doubled, then the angle of elevation of its top will not be doubled.

Updated on 10-Oct-2022 13:28:58