✓ Board-verified
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…
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)
(a)
Determine height of the water tank.
OR
(b)
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 \(\displaystyle =\mathrm{h}+\mathrm{d}=(54+18 \sqrt{3}) \mathrm{m}\)
OR
(iii)(b)
\(\displaystyle \angle \mathrm{WAC}=30^{\circ}, \tan 30^{\circ}=\frac{1}{\sqrt{3}}=\frac{\mathrm{WC}}{54} \Rightarrow \mathrm{WC}=18 \sqrt{3} \mathrm{~m}\)
\(\displaystyle \sin 45^{\circ}=\frac{1}{\sqrt{2}}=\frac{\mathrm{h}}{\mathrm{x}} \Rightarrow \mathrm{x}=\mathrm{h} \sqrt{2} \Rightarrow \mathrm{x}=54 \sqrt{2} \mathrm{~m}\)
All Some Applications of Trigonometry questions2026 question paperNCERT solutions: Some Applications of TrigonometryPractice Some Applications of Trigonometry →
More from Some Applications of Trigonometry
- From the top of an 8 m high building, the angle of elevation of the top of a cable tower is 60^° and the angle of depression of its foot is 45^°.…2022
- From a point on the ground, which is 30 m away from the foot of a vertical tower, the angle of elevation of the top of the tower is found to be 60°.…2024
- From the top of a 45 m high light house, the angles of depression of two ships, on the opposite side of it, are observed to be 30° and 60°. If the…2024
- The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of…2022
- A boy standing on a horizontal plane is flying a kite with a string of length 60 m, at an angle of elevation of 30°. Another boy standing on the roof…2026
- Two boats are sailing in the sea 80 m apart from each other towards a cliff AB. The angles of depression of the boats from the top of the cliff are…2022
- The angle of elevation of the top of a building from a point A, on the ground, is 30°. On moving a distance of 24 m towards its base to the point B,…2026
- A wire is attached from a point A on the ground to the top of a pole BC, making an angle of elevation as 60^°. If AB=5 √3 m, then length of the wire…2026
CBSE Class 10 Mathematics past-paper question from the 2026 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.