The angles of depression of two ships
from the top of a light house and on the
same side of it are found to be 45° and
30°. If the ships are 200 m apart, find the
height of the light house
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D and C be given ships and AB be the lighthouse.
Let Height of light house is AB=h
In △BAC, we have:
tan45
∘
=
BC
AB
1=
BC
AB
⟹AB=BC
so, BC=h ... (1)
In triangle ADB,
tan30
∘
=
BD
AB
3
1
=
BC+200
h
3
1
=
h+200
h
[Using (1)]
h+200=h
3
h(
3
−1)=200
h=
3
−1
200
m
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