Q11 of 35 Page 219

From the top of a 300 m high light – house, the angles of depression of the top and foot of a tower have measure 30 and 60. Find the height of the tower.

Let AC be the lighthouse and ED be the tower.



Height of lighthouse = AC = 300 m


Let ED = h


Let EB be the perpendicular from E to AC.


The angles of depression of the top E and bottom D of the tower ED measures 30⁰ and 60⁰ respectively from A.


∠AEB = 30⁰


∠ADC = 60⁰


In ∆ADC,





Now, In ∆AEB,





AB = 100 m


Height of the tower ED = BC


= AC – AB


= 300 – 100


= 200 m


The height of the tower is 200m.


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