Question

The angles of depression of two ships from the top of a light house are 45° and 30°
towards east. If the ships are 100 m apart, the height of the light house is​

Answer 1

Answer:

Let 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

OR,

By rationalization and simplification, we get,

h=100(

3

+1) m.

Hi, hope it is helpful to allllll...