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Mathematics · 2022 · 4 marks
CBSE 2022 · Region 3 · Set 3 · Q11
The angle of elevation of the top Q of a vertical tower PQ from a point X on the ground is $\displaystyle 60^{\circ}$. From a point $\displaystyle \mathrm{Y}, 40 \mathrm{~m}$ vertically above X , the angle of elevation of the top Q of tower PQ is $\displaystyle 45$°. Find the height of the tower PQ and the distance PX . [Use $\displaystyle \sqrt{3}=1 \cdot 73$ ]
Marking-scheme solution
In $\displaystyle \triangle Y R Q, \tan 45^{\circ}=\frac{Q R}{Y R} \Rightarrow Q R=Y R$In $\displaystyle \triangle X P Q, \tan 60^{\circ}=\frac{P Q}{X P} \Rightarrow \sqrt{3}=\frac{P Q}{X P}$Further, $\displaystyle P R=40 \mathrm{~m}$From (i) to (iii), we get
\[\mathrm{PQ}=94.6 \mathrm{~m}, \mathrm{PX}=54.6 \mathrm{~m}
\]
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CBSE Class 10 Mathematics past-paper question from the 2022board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.