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Byju's Answer
Standard X
Mathematics
Angle of Elevation
Question 16 T...
Question
Question 16
The angle of elevation of the top of a vertical tower from a point on the ground is
60
∘
. From another point 10m vertically above the first, its angle of elevation is
45
∘
. Find the height of the tower.
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Solution
Let the height the vertical tower, OT = H
And OP = AB = x m
Given that, AP = 10 m
And
∠
T
P
O
=
60
∘
,
∠
T
A
B
=
45
∘
Now, in
Δ
T
P
O
,
t
a
n
60
∘
=
O
T
O
P
=
H
x
⇒
√
3
=
H
x
⇒
x
=
H
√
3
...(i)
And in
Δ
T
A
B
,
t
a
n
45
∘
=
T
B
A
B
=
H
−
10
x
⇒
1
=
H
−
10
x
⇒
x
=
H
−
10
⇒
H
√
3
=
H
−
10
[from Eq. (i)]
⇒
H
−
H
√
3
=
10
⇒
H
(
1
−
1
√
3
)
=
10
⇒
H
(
√
3
−
1
√
3
)
=
10
∴
H
=
10
√
3
√
3
−
1
.
√
3
+
1
√
3
+
1
[By rationalization]
=
10
√
3
(
√
3
+
1
)
3
−
1
=
10
√
3
(
√
3
+
1
)
2
⇒
=
5
√
3
(
√
3
+
1
)
=
5
(
√
3
+
3
)
m
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Q.
The angle of elevation of the top of a vertical tower from a point on the ground is 60°. From another point 10 m vertically above the first, its angle of elevation is 30°. Find the height of the tower. [CBSE 2011]