Question

The angle of elevation of the top of a tower is30° if the height of the tower is doubled then the angle of elevation of its top will also be doubled?

Answer 1

No the angle of elevation of top will not be doubled.

It can be understood by the following pic.....↓↓↓



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Answer 2

$\sf \: Solution -$

${ \underline{ \underline {\sf \: Given:-}}}$

$\sf :\implies \: Angle \: of \: elevation \: = 30^{o}$

Let

$\sf : \implies \: Height \: of \: tower \: = h \: \: \: and \: \: distance \: = \: x \:</p><p>$

$\sf \implies \: \tan30 \degree = \dfrac{h}{x} \: \: \: \: \: \: \: where \: \: tan30 \degree = \dfrac{1}{ \sqrt{3} }</p><p>$

By putting the value we get,

$\sf \implies \: \dfrac{1}{ \sqrt{3} } = \dfrac{h}{x}$

Now height is doubled = 2h

$\sf \implies \: \tan\theta = \dfrac{2h}{x}$

Its given

$\sf \implies \: \dfrac{h}{x} = \dfrac{1}{ \sqrt{3} } \: \: \: so \: put \: the \: value \:</p><p>$

we get,

$\sf \implies \: \tan\theta = \dfrac{2}{ \sqrt{3} }$

When Θ is double

$\sf \implies \: \theta = 30 \degree \: \implies2 \theta = 2 \times 30 = 60</p><p>$

now we know that

$\sf \implies \: \tan60 \degree = \sqrt{3} \implies \sqrt{3} \not = \dfrac{2}{ \sqrt{3} }$

So our conclusion is when height is double Θ will be not doubled.