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.