The horizontal distance between two buildings is 70 m. The angle of depression of the top of the first building when seen from the top of the second building is 45°. If the height of the second building is 120 m, find the height of the first building.
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Answer:
The horizontal distance between two towers is 60 m and angular depression of the top of the first as seen from the second, which is 150 m in height, is 30
0
. The height of the first tower is
A
(150+20
3
) m
B
(150+15
3
) m
C
(150−20
5
) m
D
(150−20
3
) m
MEDIUM
Answer
Let AB and CD be the two towers
Height of the second tower, AB =150m and
Distance between two towers BD =60m
Let's assume the height of the first tower is h m.
We know, In right angled △,
tan(Θ)=
Adjacent
Opposite
tan30
0
=
EC
AE
tan30
0
=
60
150−h
.....[AE=AB-ED] and [EC=BD=60]
⇒
3
1
=
60
150−h
⇒h
3
=150
3
−60
⇒h=150−20
3
The height of the first tower is 150−20
3
m
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