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The Unknown Side (Posted on 2002-07-01) Difficulty: 3 of 5
ABC is a triangle:
  • Angle A < 90.
  • D is a point on BC such that BD = DC.
  • M is a point on BC such that AM is perpendicular to BC.

    If
  • AD = 10,
  • BC = 12 and
  • MC = 11
    find the length of AC.
  • See The Solution Submitted by Dulanjana    
    Rating: 2.9091 (11 votes)

    Comments: ( Back to comment list | You must be logged in to post comments.)
    Question Why Angle A? | Comment 3 of 15 |
    The problem gives us that angle A is acute. While we can use the law of cosines to solve for A and verify that statement, the important thing to know is whether angle C is acute. If angle C is obtuse, then MD is no longer 5, but is 16.

    Unless that is the point: if the problem as Charadenine has broken it down and Friedlinguini has solved it requires angle A to be 90 or more, then we have the wrong triangle and must work with angle C being obtuse.
      Posted by TomM on 2002-07-01 08:41:18
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