36. 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.

Question

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)

Sapling Academy · Accepted Answer

(i) Relation between d and y:
 
In Δ AXW, sin 30 = $\frac{AX}{AW}$
 
∴ $\frac{1}{2} = \frac{d}{y}$
 
∴ y = 2 d ......... (i)
 
Therefore the relation between d and y is y = 2 d.
 
(ii) Value of h: 
 
In Δ BXW, tan 45 = $\frac{BX}{XW} = \frac{BX}{AC}$
 
∴ 1 = $\frac{h}{54}$
 
∴ 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 = $\frac{AX}{XW} = \frac{AX}{AC}$
 
∴ $\frac{1}{\sqrt 3} = \frac{d}{54}$
 
∴ d = $\frac{54}{\sqrt 3} = \frac{18 (3)}{\sqrt 3}$
 
∴ 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 = $\frac{XW}{BW}$
 
∴ $\frac{1}{\sqrt 2} = \frac{54}{x}$
 
∴ 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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