Question

The angles of elevation of the top of a tower from two points distant s and t from its foot are complementary. Then the height of the tower is:

(A) st                                                                                    

(B) s2t2

(C) √st                                                                 

(D) s/t

​

Answer 1

Answer:

$(c) \sqrt{st}$

Step-by-step explanation:

Let the height of tower be h.

Construct figure according to given information as,

$\tan( \theta ) = \frac{ac}{bc}$

$= > \tan( \theta ) = \frac{h}{s}...........(i)$

$\tan(90 - \theta ) = \frac{ac}{pc}$

$= > \cot( \theta ) = \frac{h}{t} ......(ii)$

MULTIPLYING, EQUATION (i) and (ii), WE GET

$\tan( \theta ) \times \cos( \theta ) = \frac{h}{s} \times \frac{h}{t}$

$= > 1 = \frac{ {h}^{2} }{st}$

$= > h = \sqrt{st}$

hope it's helps you ❤️

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.