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Byju's Answer
Standard X
Mathematics
Calculating Heights and Distances
The angle of ...
Question
The angle of elevation of the top of a hill at the foot of the tower is
60
∘
and the angle of elevation of the top of the tower at the foot of the hill is
30
∘
. If the tower is
50
m high, what is the height of the hill?
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Solution
Let the height of the hill,
C
D
be
h
m
.
Height of the tower,
A
B
=
50
m
.
In
△
B
C
D
,
tan
60
o
=
C
D
B
C
⇒
√
3
=
h
B
C
⇒
B
C
=
h
√
3
-------- ( 1 )
In
△
A
B
C
,
tan
30
o
=
A
B
B
C
⇒
1
√
3
=
50
B
C
∴
B
C
=
50
√
3
-------- ( 2 )
Comparing ( 1 ) and ( 2 ), we get
⇒
h
√
3
=
50
√
3
⇒
h
=
50
√
3
×
√
3
∴
h
=
150
m
Thus, the height of the hill is
150
m
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