Q) Gadisar Lake is located in the Jaisalmer district of Rajasthan. It was built by the King of Jaisalmer and rebuilt by Gadsi Singh in 14th century. The lake has many Chhatris. One of them is shown below:

Observe the picture. From a point A, h m above from water level, the angle of elevation of top of Chhatri (point B) is 45 and angle of depression of its reflection in water (point C) is 60. If the height of Chhatri above water level is (approximately) 10 m, then:

(a) draw a well-labelled figure based on the above information.

(b) find the height (h) of the point A above water level (Use √3 = 1.73)

Ans:

(a) Diagram for this question:

Here, Line EF is water level, BE is the Chhatri 10 m above the water level and EC is its reflection 10 m down the water level. A is h m above the water level. From A Point B and Point C are being seen.

b) Calculation for the Height of point A above water level:

Let ‘s start with Δ ADB,

tan ∠ DAB = 

∴ tan 45° = 

∴ d = 10 – h ……….. (i)

Next in Δ ADC,

tan ∠ DAC = 

∴ tan 60° =

∴ √3 =

∴ d = ………. (ii)

From equations (i) and (ii), we compare values of d:

10 – h =

 √3 (10 – h)  = 10 + h

10 (√3 – 1) = h (√3 + 1)

∴ h =

∴ h =              (∵ (a + b) ( a – b) = a² – b² )

∴ h =  

∴ h = 5 (√3  – 1) ² = 5 (1.73  – 1) ²

∴ h = 5 x 0.73 x 0.73 = 2.66 m

Therefore, the height of point A above the water level is 2.66 m