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Triangle Bisection question

  1. May 11, 2010 #1
    Given triangle ABC. And given that it’s a common 3-4-5 right triangle. (this still qualifies as a scalene)

    So

    AB = 4

    BC = 3

    AC = 5 is the hypotenuse

    If Angle A was bisected, do the two newly formed triangles have the same area? And would the bisecting line hit the midpoint of BC?

    Is there a triangle law that applies to this question? My inital thought is that the bisecting angle line doen't not necessaily cross the midpoint of BC. looking for a proof or any help.

    Thanks!
     
  2. jcsd
  3. May 11, 2010 #2

    Mark44

    Staff: Mentor

    Angle A = arctan(3/4), so the bisected angle is half of that. Let D be the point where the angle bisector hits BC. Since you know angle DAB, angle BDA is the complement of angle DAB. Now you know all three angles (angle ABC is a right angle), and one side (AB = 4), so you can use the Law of Sines to find the other side, BD. Hopefully you can take it from there.
     
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