Case Study - 2:

Gadisar Lake is located in the Jaisalmer district of Rajasthan. It was built by the King of Jaisalmer and rebuilt by Gadsi Singh in $14^{th}$ century. The lake has many Chhatris. One

Question

Case Study - 2:

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

[IMAGE_1]

Observe the picture. From a point A $8$ 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 $\sqrt{3} = 1.73$)

Accepted Answer

Step 1: Well-labelled figure showing point A at height h above water, B at top of Chhatri (10-h above A), C as reflection (10+h below A), with angles 45° and 60°, horizontal distance x
Step 2: (b) $	an 45° = 1 = \frac{10 - h}{x} \Rightarrow x = 10 - h$ ... (i)
Step 3: $	an 60° = \sqrt{3} = \frac{10 + h}{x} \Rightarrow x = \frac{10 + h}{\sqrt{3}}$ ... (ii)
Step 4: From (i) and (ii): $10(\sqrt{3} - 1) = h(\sqrt{3} + 1) \Rightarrow h = \frac{10(\sqrt{3} - 1)^2}{2} = 2.67$ m or $2.7$ m

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