The length of the shadow of a vertical tower on level ground

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The length of the shadow of a vertical tower on level ground increases by 10 metres when the altitude of the sun changes from 45° to 30°. Then the height of the tower is

AB = Tower = h metre
∠BDA = 30°
∠ACB = 45°
CD = 10 metre
From ∆ABC,

tan45° =	AB
	BC

⇒ 1 =	h	⇒ h = x
	x

⇒ √3h = h +10 [∵ h = x ]
⇒ √3h - h = 10
⇒ h( √3 - 1) = 10

⇒ h =	10	=	10	×	√3 + 1
	√3 - 1		√3 - 1		√3 + 1

=	10(√3 + 1)	= 5(√3 + 1) metre
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