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Mathematics · 2026 · 4 marks
CBSE 2026 · Region 5 · Set 1 · Q38
Elevated water storage tanks are built to store and supply water to nearby colonies. In the diagram given above, AB is an elevated water tank and CD is a nearby multistorey building. The building is $\displaystyle 54$ metres away from the water tank. From a window ( W ) of the building, the angle of elevation of top of the tank is $\displaystyle 45$° and angle of depression of its foot is $\displaystyle 30$°.(i)Write a relation between d (the height of window) and y.(ii)Determine the value of h.(iii)Determine height of the water tank.Find the value of $\displaystyle x$ and height of the window above ground level.
Elevated water storage tanks are built to store and supply water to nearby colonies. In the diagram given above, AB is an elevated water tank and CD is a nearby multistorey building. The building is $\displaystyle 54$ metres away from the water tank. From a window ( W ) of the building, the angle of elevation of top of the tank is $\displaystyle 45$° and angle of depression of its foot is $\displaystyle 30$°.
(i)
Write a relation between d (the height of window) and y.
(ii)
Determine the value of h.
(iii)
Determine height of the water tank.
Find the value of $\displaystyle x$ and height of the window above ground level.
Marking-scheme solution
(i) \(\displaystyle \sin 30^{\circ}=\frac{1}{2}=\frac{\mathrm{d}}{\mathrm{y}} \Rightarrow 2 \mathrm{~d}=\mathrm{y}\)
(ii) \(\displaystyle \tan 45^{\circ}=1=\frac{\mathrm{h}}{\mathrm{WX}}=\frac{\mathrm{h}}{54} \Rightarrow \mathrm{~h}=54 \mathrm{~m}\)
(iii) (a) \(\displaystyle \tan 30^{\circ}=\frac{1}{\sqrt{3}}=\frac{\mathrm{d}}{54} \Rightarrow \mathrm{~d}=18 \sqrt{3} \mathrm{~m}\)
Height of the tank \(\displaystyle =\mathrm{h}+\mathrm{d}=(54+18 \sqrt{3}) \mathrm{m}\)
(iii)
\(\displaystyle \angle \mathrm{WAC}=30^{\circ}, \tan 30^{\circ}=\frac{1}{\sqrt{3}}=\frac{\mathrm{WC}}{54} \Rightarrow \mathrm{WC}=18 \sqrt{3} \mathrm{~m}\)
\(\displaystyle \sin 45^{\circ}=\frac{1}{\sqrt{2}}=\frac{\mathrm{h}}{\mathrm{x}} \Rightarrow \mathrm{x}=\mathrm{h} \sqrt{2} \Rightarrow \mathrm{x}=54 \sqrt{2} \mathrm{~m}\)
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CBSE Class 10 Mathematics past-paper question from the 2026board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.