The horizontal distance between two towers is 70 m. The angles of depression of the top of the first tower, when seen from the top of the second tower is 30°. If the height of the second tower is 120 m, find the height of the first tower.
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Answer:
53.42m.
Step-by-step explanation:
Let AB and CD are two towers.
BD=120m=EC, ∠ACE=30
o
, ∠CBD=24
o
.
In right angle △CBD,
tan24
o
=
BD
CD
=
120
CD
CD=120×0.4452
=53.42m
In right angle △ACE,
tan30
o
=
EC
AE
=
120
AE
AE=120×0.5773
=69.28m
AB=AE+EB
=AE+CD [EB=CD]
=69.28+53.42
=122.7m
Height of 1
st
tower is 122.7m and 2
nd
tower is 53.42m.
hope it helps
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