Answer :

Let AB be the building = 60 m

And CE be the tower = h m

So, difference between the heights of the building and the tower = DE

And the distance between them = BC

Consider right angled ΔABC,

⇒ tan60° = AB/BC

⇒ √3 = 60/BC

⇒ BC = 60/√3

Rationalizing the denominator,

⇒ BC = 60(√3)/√3(√3)

= 60√3/3

∴ BC = 20√3 m = 20(1.73) = 34.6 m

BC = AD

Consider right angled ΔADE,

⇒ tan30° = DE/AD

⇒ 1/√3 = DE/20√3

⇒ DE = 20√3 / √3

∴ DE = 20 m

Ans. The difference between the heights of the building and the tower DE is 20 m and the distance between them BC is 34.6 m.

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