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NTSE Stage 2 SAT 2018 Exam Question Paper
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© examsnet.com
Question : 48
Total: 100
A vertical pole of height 10 metres stands at one corner of a rectangular field. The angle of elevation of its top from the farthest corner is 30º, while that from another corner is 60º. The area (in
m
2
) of rectangular field is
200
√
2
3
400
√
3
200
√
2
√
3
400
√
2
√
3
Validate
Solution:
Let PQRS be the rectangular field with length l and width b and RT be the vertical pole.
In ΔPRT
tan
30
∘
=
R
T
P
R
1
√
3
=
10
P
R
P
R
=
√
l
2
+
b
2
=
10
√
3
I
2
+
b
2
=
100
×
3
=
300
.....(1)
In ΔSRT
tan
60
∘
=
10
S
R
→
√
3
=
10
S
R
S
R
=
10
√
3
=
l
→
l
2
=
100
3
......(2)
Use equation (2) in (1),then
b
2
=
300
−
100
3
=
800
3
Now,
I
2
b
2
=
100
3
×
800
3
=
80000
9
l
b
=
√
80000
9
=
200
√
2
3
Hence, the required area of rectangular field is
200
√
2
3
© examsnet.com
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