Q29 of 47 Page 1

From a point on the ground, the angle of elevation of the top of a tower is observed to be 60°. From a point 40m vertically above the first point of observation, the angle of elevation of the top of the tower is 30°. Find the height of the tower and its horizontal distance from the point of observation.


The diagram represents the above problem, with PQ as tower and X any Y as points.


In △XQP





Also, XY = 40 m implies RP = 40 m


QR + RP = QP


QR = QP - RP = (QP - 40) m


In △QYR




IMPLIES


[FROM 2 AND YR = XP]





XP = 20(1.73) = 34.6 m


i.e. distance of tower from the point X is 34.6 m


and


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