construct the angle of 45 degrees at the initial point
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Let the height of the tree be y and width of the river be x and CD = 40 m
In ΔABD, tan 300 =
A
x
+
40
⇒ x+40 = y
√
3
………..(i)
In ΔABC,
tan 600 =
A
=
y
x
⇒ y = x
√
3
……………(ii)
Putting the value of y from (ii) to (i)
x+40= [x
√
3
]
√
3
= 3x
40 = 2x
⇒ x= 20
y = x
√
3
= 20
√
3
Height of the tree = 20
√
3
m
Width of the river = 20 m.
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