Question

A man observes from the top of a 50m high lighthouse from the sea level, the angles of depression of two ships are 45°and 60° . if one ship is exactly behind the other on the same side of the light house, then find the distance between the two ships.​

Answer 1

Step-by-step explanation:

Let, height of light house from sea level (AB)=100m

Let, two ships be at the positions be C and D

In △ABC,

tan 45

∘

=

BC

AB

⟹1=

BC

100

⟹BC=100m

In △ABD,

tan 30

∘

=

BD

AB

⟹

3

1

=

BD

AB

BD=AB×

3

=100×

3

=173.2[

3

=1.732]

∴CD=BD−BC=173.2=100=73.2m

∴ the distance between two ships 73.2 m