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Mathematics · 2022 · 4 marks
CBSE 2022 · Region 1 · Set 1 · Q14
Gadisar Lake is located in the Jaisalmer district of Rajasthan. It was built by the King of Jaisalmer and rebuilt by Gadsi Singh in 14^th century.…
Gadisar Lake is located in the Jaisalmer district of Rajasthan. It was built by the King of Jaisalmer and rebuilt by Gadsi Singh in $\displaystyle 14^{\text {th }}$ century. The lake has many Chhatris. One of them is shown below :
Observe the picture. From a point $\displaystyle \mathrm{A} h \mathrm{~m}$ above from water level, the angle of elevation of top of Chhatri (point B) is $\displaystyle 45$° and angle of depression of its reflection in water (point C) is $\displaystyle 60$°. If the height of Chhatri above water level is (approximately) $\displaystyle 10$ m, then
(a)
draw a well-labelled figure based on the above information;
(b)
find the height $\displaystyle (h)$ of the point A above water level. (Use $\displaystyle \sqrt{3}=1 \cdot 73$ )
Marking-scheme solution
(b)
\(\displaystyle \tan 45^{\circ}=1=\frac{10-h}{x}\)
\[\Rightarrow x=10-h
\]
\[\tan 60^{\circ}=\sqrt{3}=\frac{10+h}{x}
\]
\[\Rightarrow x=\frac{10+h}{\sqrt{3}}
\]
Solving (i) and (ii) \(\displaystyle 10(\sqrt{3}-1)=h(\sqrt{3}+1)\)
\[\begin{aligned}
\Rightarrow h & =\frac{10(\sqrt{3}-1)^{2}}{2} \\
& =2 \cdot 67 \mathrm{~m} \text { or } 2.7 \mathrm{~m}
\end{aligned}
\]
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CBSE Class 10 Mathematics past-paper question from the 2022 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.