12. A man standing on the bank of a river
observes that the angle of elevation of the
top of a tree just on the opposite bank is 60°.
The angle of elevation is 30° from a point at
a distance y m from the bank. What is the
height of the tree?
(a) y m
(b) 2y m
√3v
(c)
(d) m
(NDA, 2011)
m
2
Answers
Answered by
1
Answer:
✌Let AB be the breadth of the river and BC be the height of the tree which makes a ∠ of 60
∘
at a point A on the opposite bank.
Let D be the position of the person after retreating 20 m from the bank.
Let AB =x metres and BC =h metres.
We know, tan(θ) = Opposite / Adjacent
From right ∠ed △ ABC and DBC,
we have tan60
∘
=
AB
BC
and tan30
∘
=
20+x
h
⇒
3
=
x
h
and
3
1
=
x+20
h
⇒h=x
3
and h=
3
x+20
⇒x
3
=
3
x+20
⇒3x=x+20⇒x=10m
Putting x=10 in h=
3
x, we get
h=10
3
=17.32m
Hence, the height of the tree =17.32 m and the breadth of the river =10 m.✌
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