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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 vertical tower from a point on the ground is
60
0
. from another point 10 m vertically above the first, its angle of elevation is
45
0
.Find the height of the tower.
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Solution
R.E.F. Image.
Height of the tower, H = (h+10)m
In
△
A
B
C
,
t
a
n
60
∘
=
h
+
10
A
B
A
B
=
h
+
10
√
3
⋯
(
i
)
In
△
D
C
O
,
t
a
n
45
∘
=
h
A
B
∴
A
B
=
h
⋯
(
i
i
)
comparing eq.(i) and (ii), we get :
h
=
h
+
10
√
3
∴
√
3
h
=
h
+
10
⇒
√
3
h
−
h
=
10
⇒
h
(
√
3
−
1
)
=
10
∴
h
=
10
√
3
−
1
Height of tower = h + 10
=
10
√
3
−
1
+
10
=
10
+
10
√
3
−
10
√
3
−
1
H
=
10
√
3
√
3
−
1
m
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Q.
From a point on the ground, the angle of elevation of the top of a tower is observed to be
60
∘
. From a point 40
m
vertically above the first point of observation, the angle of elevation of the top of the tower is
30
∘
. Find the height of the tower and its horizontal distance from the point of observation.
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