Question

35. As observed from the top of a 75 m high light house above the sea level, the angles of
depression of two ships are 300 and 450 respectively if one ship is exactly behind the
other on the same side of the light house and in the same straight line, find the distance
between the two ships. (use V3 = 1.732).​

Answer 1

Answer:

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

solution