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

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• Feb 1, 2011
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, Luï¿½s 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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