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Q.

A vertical pole of height 10metres stand at one corner of a rectangular field. The angle of elevation of its top from the farthest corner is 30, while that from another corner is 60. Find the area (in m2) of the rectangular field.


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a

20023 m2

b

4003 m2

c

20023 m2

d

40023 m2 

answer is A.

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Detailed Solution

Given that a vertical pole of height 10metres stand at one corner of a rectangular field. The angle of elevation of its top from the farthest corner is 30, while that from another corner is 60.
Question ImageIn right triangle AEC,
tan30=10AC 10AC=13 AC=103m From the figure, the length of the rectangle is AB and breadth is BC.
Using pythagoras theorem in triangle ABC, where AC is diagonal,
l2+b2=AC=103m  -----------(i)
In triangle DCE,
tan60=10DC=3 DC=103=l l2=1003                                   ----------(ii)
b2=AC2-l2
b2=300-1003         [From (i) and (ii)]
b2=8003 b=8003 Area=l×b
Area=8003×103
Area=10×2×1023
Area=20023
So, the area of field is 20023m2.
Hence, the correct option is 1.
 
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