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A vertical tower sands on a horizontal p...

A vertical tower sands on a horizontal plane and is surmounted by a vertical flag staff of height `hdot` At a point on the plane, the angles of elevation of the bottom and the top of the flag.

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Let AB be a tower and BC be the flagstaff.
Let O be the observer.
Now, `angleAOB=alpha,angleAOC=beta" and " BC=h`
Let AB = H and OA = x
In `Delta OAB`
`tanalpha=(AB)/(OA)=H/xrArrx=H/(tanalpha) …(1)`
In `Delta OAC`
`tan beta=(AC)/(OA)=(H+h)/xrArrx=(H+h)/(tanbeta) ...(2)`
From equations (1) and (2), we get
`rArr H/(tanalpha)=(H+h)/(tanbeta)`
`rArr H tanbeta=Htanalpha+h" "tanalpha`
`H(tanbeta-tanalpha)=h" "tanalpha`
`rArr H=("h "tanalpha)/(tanbeta-tanalpha)`
`:." Height of the tower "=("h " tanalpha)/(tanbeta-tanalpha)`
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