A girl 1.5 m tall is standing at some distance from a 30 m high tower. The angle of elevation from her eye to the top…

CBSE Class 10 Maths PYQ · Applications of Trig · Double Triangle · 5 Marks · March 2025 · Standard

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635 Marks · March 2025 · Standard
A girl $1.5$ m tall is standing at some distance from a $30$ m high tower. The angle of elevation from her eye to the top of the tower increases from $30^\circ$ to $60^\circ$ as she walks towards the tower. Find the distance she walked towards the tower.
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Correct figure ($1$ mark)
$AF = 30 - 1.5 = 28.5$ m ($1/2$ mark)
In right $\triangle AFE$
$\frac{28.5}{EF} = \tan 60^\circ = \sqrt{3}$
$\Rightarrow EF = \frac{28.5}{\sqrt{3}}$ m ($1$ mark)
In right $\triangle ADF$
$\frac{28.5}{DF} = \tan 30^\circ = \frac{1}{\sqrt{3}}$
$\Rightarrow DF = 28.5 \sqrt{3}$ m ($1$ mark)
Distance travelled by the girl towards the tower, $DE = DF - EF$
$= 28.5 \sqrt{3} - \frac{28.5}{\sqrt{3}}$ ($1$ mark)
$= \frac{57}{\sqrt{3}} = 19 \sqrt{3}$ m or $32.91$ m approx. ($1/2$ mark)
Distance travelled by girl towards the tower is $19 \sqrt{3}$ m or $32.91$ m.
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