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Question
The angle of elevation of the top of an unfinished tower from a point at a distance of 80 m from its base is 30°. How much higher must the tower be raised so that its angle of elevation at the same point may be 60°?
Solution
Let AB be the unfinished tower and C be the top of the tower when finished, Let P be a point 80 m from the foot A.
In ΔBAP,
`tan 30^circ = (AB)/(AP)`
`=> 1/sqrt(3) = (AB)/(80)`
`=> AB = 80/sqrt(3) = 46.19 m`
In ΔCAP,
`tan 60^circ = (AC)/(AP)`
`=> sqrt(3) = (AC)/(80)`
`=> AC = 80sqrt(3) = 138.56 m`
Therefore, the tower must be raised by (138.56 – 46.19) m = 92.37 m
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