The shadow of a tower when the angle of elevation of the

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The shadow of a tower when the angle of elevation of the sun is 45°, is found to be 10 metre longer than when it was 60°. The height of the tower is

1. 5 (√3 - 1) metre
2. 5 (3 + √3) metre
3. 10 (√3 - 1) metre
4. 10 (√3 + 1) metre

AB = Height of tower
= h metre
BC = Length of shadow when ∠BCA = 60° = x metre
BD = Length of shadow when ∠ADB = 45° = (x + 10) metre
In ∆ABC,

tan 60° =	AB
	BC

⇒ √3 =	h
	x

⇒ h = 3 x metre ..... (i)
In ∆ABD,

tan 45° =	AB	⇒ 1 =	h
	BD		x + 10

⇒ h = x + 10 ⇒ h =	h	+ 10
	√3

⇒ h -	h	= 10
	√3

⇒	√3h - h	= 10
	√3

⇒ h(√3 - 1) = 10√3
+ 1)

⇒ h =	10√3	=	10√3(√3 + 1)
⇒ h =	√3 - 1	=	(√3 - 1)(	√3

= 5(3 + √3) metre