The horizontal distance between two Towers is 60m the angle 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 90m find the height of the first Tower.
USE ROOT 3= 1.732
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Step-by-step explanation:
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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