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19810[EMHL] Re: TRIANGLE CONSTRUCTION A, a, Sum_of _altitudes

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  • Antreas
    Feb 1, 2011
    • 0 Attachment
      Dear Luis

      Thanks.

      For the problem: A, b, h_a + h_b, I think there is no
      R&C construction.

      We have this system of equations:

      h_a + h_b = bsinC + csinA = bsinC + (bsinCsinA/sinB) =

      = (bsinC/sinB)(sinB + sinA)

      sinA = sinBCosC + cosBsinC

      sin^2B + cos^2B = 1

      sin^2C + cos^2C = 1

      (four equations with four unknowns: sinB,sinC,cosB,cosC)

      Antreas



      --- In Hyacinthos@yahoogroups.com, Lu�s Lopes <qed_texte@...> wrote:
      >
      >
      > Dear Hyacinthists, Antreas,
      >
      > Very nice, Antreas.
      >
      > There is a typo in your link. Let h_a + h_b + h_c = h.
      > Then
      >
      > bc+ca+ab=2R.h=k^2.
      >
      > And how about (A,b,h) ?
      >
      > h_c is known.
      >
      > Best regards,
      > Luis
      >
      >
      > To: Hyacinthos@yahoogroups.com
      > From: anopolis72@...
      > Date: Tue, 1 Feb 2011 12:48:19 +0200
      > Subject: [EMHL] Re: TRIANGLE CONSTRUCTION A, a, Sum_of _altitudes
      >
      > Solutions:
      >
      >
      >
      > http://anthrakitis.blogspot.com/2011/02/triangle-construction-a-ha-hb-hc.html
      >
      >
      >
      > On Fri, Jan 28, 2011 at 12:07 PM, Antreas Hatzipolakis <anopolis72@...
      >
      > > wrote:
      >
      >
      >
      > > To construct triangle ABC if are given A, a, h_a + h_b + h_c = h.
      >
      > >
      >
      > > APH
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