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  • If the height of a tower and the distance of the point of observation from its foot,both, are increased by 10%, then the angle of elevation of its top remains unchanged.

If the height of a tower and the distance of the point of observation from its foot,both, are increased by 10%, then the angle of elevation of its top remains unchanged.

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Answer.          [True]             
Solution.        According to question
           

In case-1. Height is H and observation distance is a.
In case-2, both height and observation distance is increased by 10%.
In case -1
\tan \theta _{1}= \frac{H}{a}         \left ( \because \tan \theta = \frac{perpendicular}{Base} \right )  .....(1)
In case -2
\tan \theta _{2}= \frac{H+\frac{H}{10}}{a+\frac{a}{10}}
= \frac{\frac{11H}{10}}{\frac{11a}{10}}= \frac{11H}{10}\times \frac{10}{11a}= \frac{H}{a}
\tan \theta _{2}= \frac{H}{a} \cdots \left ( 2 \right )
from equation (1) and (2) we observe that \theta _{1}= \theta _{2}
Hence the given statement is true.

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