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From the top of a tower h m high, angles...

From the top of a tower h m high, angles of depression of two objects, which are in line with the foot of the tower are `alpha` and `beta(betagtalpha)`. Find the distance between the two objects.

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Let AB be a tower of height 'h' m. From the top 'A' of the tower, the angle if depression of two objects D and C are `alpha " and " beta` respectively.
In `DeltaABC`
`tanbeta=(AB)/(BC)=h/(BC)`
`rArr BC=h/(tanbeta)=hcot beta ...(1)`
In `DeltaABD`
`tanalpha=(AB)/(BD)=h/(BD)`
`rArr BD=h/(tanalpha)=hcotalpha ...(2)`
Subtract equation (1) from (2), we get
`BD-BC=h cotalpha-hcotbeta`
`rArr CD=h(cotalpha-cotbeta)`
`:. " The distance between the objects `=h(cotalpha-cotbeta)m.`
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