The height of the lighthouse AC = 120 m. The observer is at C. The ship at B makes an angle of depression 15° Taking AB = x In right-angled triangle BAC tan15°=
120
x
tan(45−30)=
120
x
tan45−tan30
1+tan45tan30
=
120
x
⇒
1−
1
√3
1+
1
√3
=
120
x
⇒x(√3−1)=(√3+1)120 ⇒
√3−1
√3+1
=
120
x
⇒x=
120(√3+1)
√3−1
120(√3+1)
√3−1
×
√3+1
√3+1
=
120(3+1+2√3)
3−1
=
120(4+2√3)
2
=120(2+√3) =120×3.7 =444m Hence, option (3) is correct.