Q

# Need explanation for: - Trigonometry - JEE Main

The angle of elevation of the top of a vertical tower from a point P on the horizontal ground was observed to be . After moving a distance 2 metres from P towards the foot of the tower, the angle of elevation changes to . Then the height (in metres) of the tower is :

• Option 1)

• Option 2)

• Option 3)

• Option 4)

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As we learnt in

Height and Distances -

The height or length of an object or the distance between two distant objects can be determined with the help of trigonometric ratios.

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$In \bigtriangleup APB, \: tan\alpha =\frac{AB}{BP}$

$\Rightarrow BP=\frac{h}{\tan \alpha }=\frac{h\cos \alpha }{\sin \alpha }$

$In \bigtriangleup AQB, \: tan\beta =\frac{AB}{BQ}$

$\Rightarrow BQ=\frac{h\cos \beta }{\sin \beta }$

Now, PQ=2

$\Rightarrow PB-QB=2$

$\Rightarrow h\left [ \frac{\cos \alpha }{\sin \alpha } -\frac{\cos \beta }{\sin \beta }\right ]=2$

$\Rightarrow h\frac{\left [ \sin (\beta -\alpha ) \right ]}{\sin \alpha \: \sin \beta }=2$

$\Rightarrow h=\frac{2\sin \alpha \sin \beta }{\sin \left ( \beta -\alpha \right )}$

Option 1)

This option is correct

Option 2)

This option is incorrect

Option 3)

This option is incorrect

Option 4)

This option is incorrect

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