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From the top of a tower 100m high, a man...

From the top of a tower `100m` high, a man observes two cars on the opposite sidesof the tower and in same straight line with itsbase, with angles of depressoin `30^(@)` and `45^(@)` respectively. Find the distance between the cars . [Take `sqrt(3) = 1.732`]

Text Solution

Verified by Experts

The correct Answer is:
`273.2 m`
From right `DeltaBAD`, we have
`(AD)/(AB) = cot 45^(@) = 1 rArr (AD)/(100 m) rArr AD = 100 m`.
From right `DeltaBAC`, we have
`(AC)/(AB) = cot 30^(@) = sqrt(3) rArr (AC)/(100m) = sqrt(3)`.
`rArr Ac = (100 xx 1.732) m = 173.2 m`.
`:.` distance between the cars.
`=(173.2 + 100) m =273.2 m`.
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