Question

PQR is a triangular park with PQ=PR=200m. A T.V 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 degrees then the height of the tower in (m )is??

Answer 1

hey is the answer 5$\sqrt{2}$? 

Answer 2

Answer: The height of tower is 100 meter.

Step-by-step explanation:

Let, the height of the tower is shown by the line segment ST,

Where T is the mid point of the side QR of the triangle PQR,

Since, By the below diagram,

In triangle PST,

$tan45^{\circ} = \frac{ST}{PT}$

$\implies ST = PT$

Now, in triangle QST,

$tan30^{\circ}=\frac{ST}{QT}$

$\implies \sqrt{3}=\frac{ST}{QT}$

$\implies QT= ST\sqrt{3}$

$\implies QT = PT\sqrt{3}$

Now, in triangle PQT,

$PQ^2=PT^2+QT^2$

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

$40000 = 4PT^2$

$10000 = PT^2\implies PT = 100$

⇒ ST = PT = 100 meters.

⇒ The height of the tower is 100 meters.