2. A person standing on the bank of a river, observes that the angle of elevation of the
top of a tree, standing on the opposite bank is 45°. When he moves 40 m away from
the bank, he finds the angle of elevation to be 30°. Find the height of the tree and the
width of the river. (V3 = 1.732)
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Explanation:
Let CD=h be the height of the tree and BC=x be the breadth of the river.
From the figure ∠DAC=30
∘
and ∠DBC=60
∘
In right angled triangle △BCD,tan60
∘
=
BC
DC
⇒
3
=
x
h
⇒h=x
3
.....(1)
From the right-angled triangle △ACD
tan30
∘
=
40+x
h
⇒
3
1
=
40+x
h
⇒
3
h=40+x .......(2)
From (1) and (2) we have
3
(x
3
)=40+x
⇒3x=40+x
⇒3x−x=40
⇒2x=40
⇒x=
2
40
=20
From (1) we get h=x
3
=20
3
=20×1.732=34.64m
∴ Height of the tree=34.64 m and width of the river=20m
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