PQR is a triangular park with PQ = PR = 200m . A T.V. tower stands...

Let the height of the tower $MN$ be $h$

In $∆ QMN$

$\tan 30 ° = \dfrac{MN}{QM}$

$∴ QM = \sqrt{3}h = MR \ldots ( 1 ) { ∵ M\text{ is }\text{ the }\text{ point } QM = MR }$

Now in $\delta MNP$

$∵ ∠ MPN = ∠ NMP = 45 °$

$∴ MN = PM ( ∵$ In a triangle sides opposite to equal angles are

equal$. . . \left(2\right) )</p><p>$∴ MN = PM = h$</p><p>In$∆ PMQ$</p><p>By using Equation \left(1\right)</p><p>$PM = \sqrt{( 200{)}^{2} - ( \sqrt{3}h{)}^{2}}${By using Pythagoras theorem}</p><p>$∴ From $\left(2\right)</p><p>$h = \sqrt{( 200{)}^{2} - ( \sqrt{3}h{)}^{2}}$</p><p>$⇒ h = \sqrt{( 40000 ) - 3{h}^{2}}$</p><p>$⇒ {h}^{2} = 40000 - 3{h}^{2}${By squaring both the sides}</p><p>$⇒ 4{h}^{2} = 40000$</p><p>$⇒ {h}^{2} = 10000m$</p><p>$⇒ h = 100m$</p>$