CEMC Euclid, 2002

Algebra Difficulty 3.0 AMC 10/12 Prove it Canada

A ladder, $AB$ , is positioned so that its bottom sits on horizontal ground and its top rests against a vertical wall, as shown. In this initial position, the ladder makes an angle of $70°$ with the horizontal. The bottom of the ladder is then pushed $0.5$ m away from the wall, moving the ladder to position $A'B'$ . In this new position, the ladder makes an angle of $55°$ with the horizontal. Calculate, to the nearest centimetre, the distance that the ladder slides down the wall (that is, the length of $BB'$ ).

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