Maths Olympiad Prep

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, 2002

Algebra Difficulty 3.0 AMC 10/12 Prove it Canada

A ladder, ABAB, 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°70° with the horizontal. The bottom of the ladder is then pushed 0.50.5 m away from the wall, moving the ladder to position A′B′A'B'. In this new position, the ladder makes an angle of 55°55° with the horizontal. Calculate, to the nearest centimetre, the distance that the ladder slides down the wall (that is, the length of BB′BB').

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.