Results 1 to 4 of 4

Math Help - Iscosceles triangle

  1. #1
    mms
    mms is offline
    Junior Member
    Joined
    Jul 2009
    Posts
    67

    Iscosceles triangle

    AB=AC
    find x

    thank you
    Attached Thumbnails Attached Thumbnails Iscosceles triangle-dibujo1.jpg  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Jul 2009
    From
    Singapore
    Posts
    338
    Quote Originally Posted by mms View Post
    AB=AC
    find x

    thank you
    180^0-50^o-60^o=70^o
    the angle opposite of it is also 70^o and the other two angles are 50^o and 60^o
    the two triangles are similar, and i can't exactly remember which rule, but x would be 60^o
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570
    Hello mms
    Quote Originally Posted by mms View Post
    AB=AC
    find x

    thank you
    This is surprisingly tricky. The answer is x = 110^o, which I can prove using trigonometry, but I'm not sure whether there's a simpler explanation. My solution is this.

    Let the points on the lines AB and AC be D and E respectively, and suppose that AB = AC = y.

    Then \angle ABC = \angle ACB = 80^o (isosceles \triangle ABC)

    \Rightarrow \angle ABE = 20^o and \angle ACD = 30^o

    So using Sine Rule on \triangleís ABE and ACD:

    AE = \frac{y\sin20}{\sin140} = 0.5321y, AD = \frac{y\sin 30}{\sin130}= 0.6527y

    Now use Cosine Rule on \triangle ADE:

    DE^2 = 0.5321^2y^2 + 0.6527^2y^2 - 2\times 0.5321\times 0.6527 y^2\cos20 = 0.0564y^2

    \Rightarrow DE = 0.2376y

    \Rightarrow \sin\angle EDA = \frac{AE\sin20}{DE}=\frac{0.5321\sin20}{0.2376}=0.  9395

    \Rightarrow \angle EDA = 50^o

    \Rightarrow x = 110^o

    Perhaps someone can come up with a more direct method?

    Grandad

    PS Correction!

    Sorry, I calculated the wrong angle. It's \angle DEA that's 110^o. bjhopper is quite right. x = 140 - 110 = 30^o
    Last edited by Grandad; July 10th 2009 at 05:33 AM. Reason: Add PS
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    Joined
    Nov 2007
    From
    Trumbull Ct
    Posts
    888
    Thanks
    25

    isosceles triangle originally posted by mms

    your diagram is a bit distorted..the line forming the x angle should be oblique.this is not an easy problem.in fact it is more of a puzzle.it comes uo on the internet as the hardest / easiest problem in geometry.

    the answer is 30.proof requires construction lines sorry i cannot put drawings in this reply.other responders migth help


    bjh
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. circle/ iscosceles triangle
    Posted in the Geometry Forum
    Replies: 1
    Last Post: February 28th 2010, 01:15 PM
  2. Replies: 3
    Last Post: April 30th 2009, 07:41 AM
  3. Replies: 1
    Last Post: October 28th 2008, 07:02 PM
  4. Replies: 7
    Last Post: July 19th 2008, 06:53 AM
  5. Replies: 27
    Last Post: April 27th 2008, 10:36 AM

Search Tags


/mathhelpforum @mathhelpforum