Math, asked by khankarim2035, 11 months ago

The angle of elevation of the top T of a vertical tower from a point x is 45°.from a point T in the straightline between X and P the frot of the tower, the angle of elevation is 60°.if xy=200cm and PT=x cm calculate x.

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Answered by vanshpatel59
5

Answer:

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Answered by swethassynergy
1

Correct Question

The angle of elevation of the top T of a vertical tower from a point x is 45°.from a point Y in the straight line between 'X and P the foot of the tower', the angle of elevation is 60°.if XY=200cm and PT=X cm calculate x.

Answer:

the value of x is \frac{200\sqrt{3} }{(\sqrt{3} -1)}  \ cm .

Step-by-step explanation:

Given:

The angle of elevation of the top T of a vertical tower from a point x is 45°.

From a point Y in the straight line between 'X and P the foot of the tower', the angle of elevation is 60°.

XY=200 cm and PT=x cm.

To Find:

The value of x.

Solution:

In the right angle \triangle TPY,

tan60\textdegree=\frac{Perpendicular}{Base} =\frac{TP}{PY}

\sqrt{3} =\frac{x}{n}

n=\frac{x}{\sqrt{3} }   ------------ equation no.01.

In the right angle  \triangle TPX

tan45\textdegree=\frac{Perpendicular}{Base} =\frac{TP}{PX}

1 =\frac{x}{n+200}

x= n  +200  ------------ equation no.02.

Putting the value of n from equation no.01 to equation no.02, we get.

x= \frac{x}{\sqrt{3} }  +200

x- \frac{x}{\sqrt{3} }  =200

x(\frac{\sqrt{3} -1}{\sqrt{3} } ) =200

x=\frac{200\sqrt{3} }{(\sqrt{3} -1)}  \ cm

Hence,  the value of x is \frac{200\sqrt{3} }{(\sqrt{3} -1)}  \ cm .

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