From the top of a cliff 100-metre high, the angles of depression of the top and bottom of a tower are 45° and 60° respectively. The height of the tower is

• A. \(\frac{{100}}{3}\left( {3 - \sqrt 3 } \right)\;{\rm{metre}}\)
• B. \(\frac{{100}}{3}\left( {\sqrt 3 - 1} \right)\;{\rm{metre}}\)
• C. \(\frac{{100}}{3}\left( {2\sqrt 3 - 1} \right){\rm{metre}}\)
• D. \(\frac{{100}}{3}\left( {\sqrt 3 - \sqrt 2 } \right){\rm{metre}}\)