Height and DistanceHard
Question
If the angles of elevation 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 30o, 45o and 60o respectively, then the ratio, AB : BC, is :
Options
A.1 : √3
B.2 : 3
C.√3 : 1
D.√3 : √2
Solution
Let height of tower is ′h′
Let AB = x, BC = y , CD = z then, in ᐃAED,
tan 30o =
⇒ x + y + z = h√3
in ᐃBED, tan 45o =
⇒ y + z = h
in ᐃCED, tan 60o =
⇒ z = 
∴ x = (√3 - 1)h, y = h
, z = 
∴
⇒ AB : BC √3 : 1
Let AB = x, BC = y , CD = z then, in ᐃAED,
tan 30o =
⇒ x + y + z = h√3
in ᐃBED, tan 45o =
⇒ y + z = hin ᐃCED, tan 60o =
⇒ z = ∴ x = (√3 - 1)h, y = h
, z = ∴
⇒ AB : BC √3 : 1Create a free account to view solution
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