Saturday, January 26, 2013

Problem 848: Special Right triangle, Catheti or legs ratio 1:2, 26.5 Degrees. Double angle

Geometry Problem
Level: Mathematics Education, High School, Honors Geometry, College.

Click the figure below to see the complete problem 848.

Online Geometry Problem 848: Special Right triangle, Catheti or legs ratio 1:2, 26.5 Degrees. Double angle

Posted by Antonio Gutierrez at 3:32 PM
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6 comments:

  1. UnknownJanuary 27, 2013 at 4:41 AM

    we have tan c=c/2c
    then tanc =0.5
    c = shift tan(0.5)= 26.56

    ReplyDelete
  2. AjitJanuary 28, 2013 at 6:48 PM

    Draw a perpendicular BD from B to AC and the Let the two circles intersect in E.
    Now, AC = sqrt(5)*c while BD * AC = AB * BC or BD = (c * 2c)/(sqrt(5)*c) = 2c/sqrt(5)
    We can say that /_ACB//_ECB ~= BD/BE = 2/sqrt(5) or /_ACB = /_ECB * 2/sqrt(5) = 60/sqrt(5)
    or /_ ACB ~= 26.83281

    ReplyDelete
  3. UnknownJune 21, 2013 at 9:44 AM

    I did not get this problem
    dear antonio gutierrez can u post this soln
    my teachers the problem is immpossible

    ReplyDelete
    Replies
    1. Antonio GutierrezJune 21, 2013 at 5:33 PM

      Dear Pranav,
      I apologize for the problem (Site Temporarily Unavailable), I am looking for a solution. In the meantime you can see this problem at http://agutie.homestead.com/files/geometry/p848-special-right-triangle-cathetus-1-2-angle-26.5-degrees.htm

      Delete
  4. UnknownJune 23, 2013 at 3:00 AM

    i did not get the solution
    please help

    ReplyDelete
    Replies
    1. Antonio GutierrezJune 23, 2013 at 7:34 AM

      Problem 848 Hints
      1 Draw the cevian AD (D on AC) so that AD = DC
      2 Prove that triangle ABD is the special right triangle 3k-4k-5k (angles aprox. 37 and 53 degrees).
      3 Apply 180 degrees in isosceles triangle ADC
      Good luck

      Delete

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