The angles of depression of two ships from the top of a

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The angles of depression of two ships from the top of a light house are 60° and 45° towards east. If the ships are 300 metre apart, the height of the light house is

1. 200 (3 + √3) metre
2. 250 (3 + √3) metre
3. 150 (3 + √3) metre
4. 160 (3 + √3) metre

AB = Lamp post = h metre C and D = Positions of ships CD = 300 metre; BC = x metre ∆ACB = 60 metre; ∠ADB = 45°
In ∆ABC,

tan 60° =	AB
	BC

⇒ √3 =	h
	x

⇒ h = √3x ..... (i)
In ∆ABD,

tan 45° =	AB
	BD

⇒ 1 =	h
	x + 300

⇒ h = x + 300

⇒ h =	h	+ 300
	√3

⇒ h -	h	= 300
	√3

⇒ h -	√3h - h	= 300
	√3

⇒ h (√3 - 1) = 300√3

⇒ h =	300(√3)
	√3 - 1

=	300√3(√3 + 1)
	(√3 - 1)(√3 + 1)

=	300(3 + √3)
	2

= 150(3 + √3) metre
= 45 kmph.