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Q) 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 54 metres away from the water tank.serve the diagram and based on above information, answer the following questions:
From a window (W) of the building, the angle of elevation of top of the tank is 45° and angle of depression of its foot is 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.
(iv) Find the value of x and height of the window above ground level.
(Q 36 – 30/5/2 – CBSE 2026 Question Paper)
Ans:
(i) Relation between d and y:
In Δ AXW, sin 30 = 
∴ 
∴ y = 2 d ……… (i)
Therefore the relation between d and y is y = 2 d.
(ii) Value of h: 
In Δ BXW, tan 45 = 
∴ 1 = 
∴ h = 54
Therefore, the value of h is 54 m.
(iii) Determine height of the water tank.
Height of the tank is given by AB
∵ AB = AX + XB
∴ AB = d + h
∵ h = 54 (from part (ii) above)
∴ AB = d + 54 ….. (ii)
Let’s calculate value of d:
In Δ AXW, tan 30 = 
∴ 
∴ d = 
∴ d = 18√3 = 18 x 1.732
∴ d = 31.176
Substituting value of d in equation (ii), we get:
∴ AB = 18√3 + 54
∴ AB = 31.176 + 54 = 85.176
Therefore, the height of the water tank is 85.14 m
(iv) Find the value of x and height of the window above ground level.
A) Value of x:
In Δ BXW, cos 45 = 
∴
∴ x = 54√2 = 54 x 1.414
∴ x = 76.356 m
B) Height of the window:
From the diagram, height of the window above ground level = CW
∵ CW = AX = d
We calculated, value of d = 31.176 in part (iii)
Therefore, value of x is 54√2 m (=76.356 m) and height of the window above ground level is 18√3 m (=31.176 m)
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