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PQR is a triangular park with PQ=PR=200 m. A TV tower stands at the mid-point of QR. If the angles of elevation of the top of the tower at P,Q and R are respectively 45°,30° and 30° ,then the height of the tower (in m) is 

Answer:

Explanation:

Let height of tower TM be h

In            $\triangle PMT.\tan45^{o}=\frac{TM}{PM}$

$\Rightarrow$           $1=\frac{h}{PM}$

 $\Rightarrow$    PM=h

In $\triangle TQM, \tan30^{o}=\frac{h}{QM^{2}}$

   $QM=\sqrt{3}h$

In $\triangle PMQ $   $PM^{2}+QM^{2} =PQ^{2}$

                               $h^{2}+(\sqrt{3h})^{2} =200^{2}$

$\Rightarrow$    $4h^{2}=(200)^{2}$

$\Rightarrow$   h=100 m