Q21 of 52 Page 1

The angles of depression of the top and bottom of a tower as seen from the top of a 60√3 m high cliff are 45° and 60° respectively. Find the height of the tower.


Let’s take PQ = 60√3 be the cliff and


CD be the tower


In right ∆PQR,


Tan 60° = PQ/QR


√3 = 60√3/QR


√3 QR = 60√3


QR = 60√3/√3 = 60 m


In right ∆PTS


Tan 45° = PT/ST


1 = PT/60


PT = 60 m


Therefore;


Height of the tower,


RS = QT


= PQ – PT


= 60√3 – 60 = 60(√3 – 1)


= 60(1.73 – 1)


= 60(0.73)


= 43.8 m


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