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 `30^0`
, `45^0`
and `60^0`
respectively, then the ratio, AB : BC, is :
(1) `sqrt(3):1`
(2)
`sqrt(3):sqrt(2)`
(3)
`1:sqrt(3)`
(4)
`2"":""3`
A
`sqrt(3):1`
B
`sqrt(3):sqrt(2)`
C
`1:sqrt(3)`
D
`2:3`
Text Solution
Verified by Experts
Let ED be the tower of height h. `tan 30 ^@ = (h) /(AD) ` ` rArr AD= h sqrt( 3) ` `BD= h,CD=h/sqrt( 3)` `(AB)/(BC)=(AD- BD)/(BD-CD)` `(hsqrt(3)-h)/(h-(h)/sqrt3)=(sqrt(3)-1)/(((sqrt(3)-1)/(sqrt(3))))=sqrt(3)`
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