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Turning Object

Source:

January 5, 2009
probabilitygeometrytrigonometry

Problem Statement

An object moves 8 8 cm in a straight line from A A to B B, turns at an angle α \alpha, measured in radians and chosen at random from the interval (0,π) (0,\pi), and moves 5 5 cm in a straight line to C C. What is the probability that AC<7 AC<7? <spanclass=′latex−bold′>(A)</span> 16<spanclass=′latex−bold′>(B)</span> 15<spanclass=′latex−bold′>(C)</span> 14<spanclass=′latex−bold′>(D)</span> 13<spanclass=′latex−bold′>(E)</span> 12 <span class='latex-bold'>(A)</span>\ \frac{1}{6} \qquad <span class='latex-bold'>(B)</span>\ \frac{1}{5} \qquad <span class='latex-bold'>(C)</span>\ \frac{1}{4} \qquad <span class='latex-bold'>(D)</span>\ \frac{1}{3} \qquad <span class='latex-bold'>(E)</span>\ \frac{1}{2}
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