If the angles of elevations of the top of a tower from three collinear points A,B and C on a line leading to the foot of the tower are $$30$$∘,$$45$$∘ , and $$60$$∘ respectively, then the ratio AB:BC is

Question

If the angles of elevations of the top of a tower from three collinear points A,B and C on a  line leading to the foot of the tower are $$30$$∘,$$45$$∘ , and $$60$$∘ respectively, then the ratio AB:BC is

Infinity Learn · Accepted Answer

Let ' h ' be the height of the tower MN From ΔMCN,$$tan$$⁡$$60=hx$$⇒$$x=h$$ $$cot60$$°,and from ∆MBN,$$tan$$ $$45=hBN$$⇒$$h=BN$$⇒ $$BC=h$$−x⇒$$BC=h-hcot60$$° From ΔMAN,$$tan$$⁡$$30=hAB+h$$⇒$$AB+h=h$$ $$cot30$$°⇒ $$AB=hcot$$⁡$$30$$∘−h∴$$ABBC=hcot$$⁡$$30$$∘−$$1h1$$−$$cot$$⁡$$60$$∘$$=3$$−$$11$$−$$13=3$$∴AB:$$BC=3$$:$$1$$

$If the angles of elevations of the top of a tower from three collinear points A, B and C on a$
$line leading to the foot of the tower are 30^{\circ}, 45^{\circ}, and 60^{\circ} respectively, then the ratio$ $A B : B C is$

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If the angles of elevations of the top of a tower from three collinear points A,B and C on a line leading to the foot of the tower are 30∘,45∘ , and 60∘ respectively, then the ratio AB:BC is

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$If the angles of elevations of the top of a tower from three collinear points A, B and C on a$
$line leading to the foot of the tower are 30^{\circ}, 45^{\circ}, and 60^{\circ} respectively, then the ratio$ $A B : B C is$