a man wants to find the breadth of a river he stands on the bank and sees a mirror on the opposite bank and find the angle of elevation of its top as 45degree when he recedes 30 M and sees the top of the mirror , the angle of elevation become 30 degree find of the breadth of the
river
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1
Answer:
Step-by-step explanation:
Let BC be the height of the tree,
AB be the breadth of the river
A be the initial position of the man
D be the final potion of the man
angle CAB
=
60
°
angle CDB
=
30
°
DA
=
40
m
Let AB =
x
Let BC =
h
Consider the triangle DBC
tan
30
=
B
C
D
B
=
B
C
D
A
+
A
B
=
h
40
+
x
1
√
3
=
h
40
+
x
h
=
40
+
x
√
3
⋯
(
1
)
Consider the triangle ABC
tan
60
=
B
C
A
B
=
h
x
√
3
=
h
x
h
=
√
3
x
⋯
(
2
)
Using (2) in (1)
h
=
40
+
x
√
3
√
3
x
=
40
+
x
√
3
3
x
=
40
+
x
2
x
=
40
x
=
20
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