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From a window ( h meter above ground) th...

From a window ( h meter above ground) the angle of elevation of other house is `theta` and angle of depression is `phi`. Find the height of the house.

Text Solution

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Let A be the window of a house of height 'h'. CE be another house in front of first house.
Given that
`angleEAD=alpha" and "angle ACB=beta`
In `DeltaAED`,
`cotbeta=(BC)/(AB)=(BC)/h rArr BC=h cot beta …(1)`
In `DeltaAED`,
`tanalpha=(ED)/(AD) rArr tan alpha=(ED)/(BC) rArr tanalpha=(ED)/(BC)`
`rArr ED=BC tanalpha=htanalpha cotbeta`
Now `EC=DC+ED=h+h tan alpha cot beta`
`=(1+tanalpha cot beta)`
`:." Height of other house "=h(1+tan alpha cot beta)`
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