Question

As observed from the top of a 75 m high lighthouse from the sea-level
, the angles of
depression of two ships are 30 and 45°. If one ship is exactly behind the other on the
same side of the lighthouse, find the distance between the two ships.
​

Answer 1

Answer:

Lines PA and BD are parallel and AB is the transversal

∴∠ABD=∠PAB [Alternate angles]

So,∠ABD=30

o

Similarly,

Lines PA and BD are parallel and AC is the transversal

∴∠ACD=∠PAC [Alternate angles]

So,∠ABD=45

o

Since lighthouse is perpendicular to ground

∠ADB=90

o

In right angled triangle ACD

tan45=

CD

AD

1=

CD

75

CD=75 m

Similarly,

In a right angled triangle ABD

tan30=

BD

AD

3

1

=

BD

75

BD=75

3

m

BC+CD=75

3

BC+75=75

3

BC=75(

3

−1) m

Hence the distance between two ships id 75(

3

−1) m