Results 1 to 2 of 2

Math Help - Triangle Question

  1. #1
    Newbie
    Joined
    Oct 2009
    Posts
    5

    Triangle Question

    In a triangle ABC where <A=120 degrees, Q and P are points on BC such that BP=BA and CQ=CA, where Q lies between B and P. Prove that <PAQ=30 degrees.

    I really could use a lot of help on this one.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,738
    Thanks
    645
    Hello, TheNcredibleHulk!

    Did you make a sketch?


    In triangle ABC where \angle A=120^o,\;P and Q are points on BC
    such that: BP=BA and CQ=CA, where Q lies between B and P.
    Prove that: . \angle PAQ\,=\,30^o
    Code:
        B o
            * *
              *   *
                *  θ  *
                  *       *    Q
                    *         o    P
                      *           o
                        *       *     *
                          *   *           *
                            o  *  *  *  *  *  o C
                           A

    Draw line segment AQ.

    Let \angle B \,=\,\theta . . . Then \angle C \,=\,60-\theta


    In isosceles \Delta ABP\!:\;\angle BPA = \angle BAP

    . . \theta + \angle BPA + \angle BAP \:=\:180^o \quad\Rightarrow\quad \angle BPA \:=\:90 - \tfrac{1}{2}\theta \:=\:\angle QPA


    In isosceles \Delta CAQ\!:\;\angle CQA = \angle CAQ

    . . (60-\theta) + \angle CQA + \angle CAQ \:=\:180^o \quad\Rightarrow\quad \angle CQA \:=\:60 + \tfrac{1}{2}\theta \:=\:\angle PQA



    In \Delta APQ\!:\;\angle PAQ + \angle PQA + \angle QPA \:=\:180^o


    Therefore: . \angle PAQ + \left(90^o-\tfrac{1}{2}\theta\right) + \left(60^o +\tfrac{1}{2}\theta\right) \:=\:180^o \quad\Rightarrow\quad \angle PAQ \:=\:30^o

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Triangle Question
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: April 2nd 2010, 06:27 PM
  2. triangle question
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: November 7th 2009, 07:52 AM
  3. Triangle question
    Posted in the Geometry Forum
    Replies: 5
    Last Post: June 27th 2009, 01:50 AM
  4. triangle question
    Posted in the Geometry Forum
    Replies: 3
    Last Post: December 4th 2008, 06:04 AM
  5. Triangle question
    Posted in the Geometry Forum
    Replies: 2
    Last Post: October 22nd 2008, 01:17 PM

Search Tags


/mathhelpforum @mathhelpforum