The elevation of the top of a tower from a point on the

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The elevation of the top of a tower from a point on the ground is 45°. On travelling 60 m from the point towards the tower, the elevation of the top becomes 60°. The height of the tower (in metres) is

AB = tower = h metre
∠ACB = 45°, ∠ADB = 60°
CD = 60 metre] BD = x metre
From ∆ABC,

tan 45° =	AB
	BC

⇒ 1 =	h
	x + 60

⇒ h = x + 60 ....................(i)
From ∆ABD

tan 60° =	AB
	BD

⇒ √3 =	h
	x

⇒ h = √3x
⇒ h = √3(h - 60)
⇒ √3h - h= 60√3
⇒ h(√3 - 1) = 60√3

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

= 30√3(√3 + 1)
= 30(3 + √3) metre