If the angle of elevation of the sun decreases from 45°

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If the angle of elevation of the sun decreases from 45° to 30°, then the length of the shadow of a pillar increases by 60m. The height of the pillar is

1. 60 (√3 + 1) metre
2. 30 (√3 - 1) metre
3. 30 (√3 + 1) metre
4. 60 (√3 - 1) metre

AB = Height of pole = h metre
CD = 60 metre
In ∆ABC

tan 45° =		AB	⇒ 1 =	h
		BC		BC

⇒ BC = h metre
In ∆ABD,

tan 30° =	AB
	BD

⇒		1	=	h
		√3		h + 60

⇒ √3 h = h + 60
⇒ √3 h – h = 60
⇒ h (√3 - 1) = 60

⇒ h =	60
	√3 - 1

=		60(√3 + 1)	=	60(√3 + 1)	= 90
		(√3 - 1)(√3 + 1)		2

= 30 (√3 + 1) metre