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<p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'>Ja to zkusim taky:<o:p></o:p></span></p>
<p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'><o:p> </o:p></span></p>
<p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'>Oznacim r1 a r2 stenove uhlopricky prislusne ke stenam se
zadanymi uhly alfa a beta, resp. delky sten a, b a vysku v. Pak<o:p></o:p></span></p>
<p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'><o:p> </o:p></span></p>
<p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'>v = r1*sin(alfa) = r2*sin(beta); r2 = r1 sin(alfa)/sin(beta)<o:p></o:p></span></p>
<p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'>a=r1*cos(alfa); b=r2*cos(beta)=r1 sin(alfa)cos(beta)/sin(beta)<o:p></o:p></span></p>
<p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'><o:p> </o:p></span></p>
<p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'>nyní vime, ze a^2+b^2+v^2=r^2, takze<o:p></o:p></span></p>
<p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'><o:p> </o:p></span></p>
<p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'>r^2 = r1^2 cos^2(alfa) + r1^2 sin^2(alfa) cos^2(beta) /
sin^2(beta) + r1^2 sin^2(alfa)<o:p></o:p></span></p>
<p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'><o:p> </o:p></span></p>
<p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'>Z vyse uvedeneho vzorce jiz mame jedinou neznamou, r1, ostatní jsou
parametry. <o:p></o:p></span></p>
<p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'><o:p> </o:p></span></p>
<p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'>Ja jsem dosel (nevim, jestli me zjednodusovani je ještě spravne </span><span
style='font-size:11.0pt;font-family:Wingdings;color:#1F497D'>J</span><span
style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>) k
temto vysledkum:<o:p></o:p></span></p>
<p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'><o:p> </o:p></span></p>
<p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'>k =[sin^2(alfa) + sin^2(beta) – sin^2(alfa)sin^2(beta)] ^ 0.5 ; ^
0.5 = odmocnina, sqrt<o:p></o:p></span></p>
<p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'><o:p> </o:p></span></p>
<p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'>a = r sin(beta)cos(alfa) / k<o:p></o:p></span></p>
<p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'>b = r sin(alfa)cos(beta) / k<o:p></o:p></span></p>
<p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'>v = r sin(alfa)sin(beta) / k<o:p></o:p></span></p>
<p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'><o:p> </o:p></span></p>
<p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'>--<o:p></o:p></span></p>
<p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'>S pozdravem/with best regards<o:p></o:p></span></p>
<p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'><o:p> </o:p></span></p>
<p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'> Ing. Tomas Dresler<o:p></o:p></span></p>
<p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'><o:p> </o:p></span></p>
<p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'>mailto:dresler@hw.cz<o:p></o:p></span></p>
<p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'><o:p> </o:p></span></p>
<div style='border:none;border-top:solid #B5C4DF 1.0pt;padding:3.0pt 0cm 0cm 0cm'>
<p class=MsoNormal><b><span style='font-size:10.0pt;font-family:"Tahoma","sans-serif"'>From:</span></b><span
style='font-size:10.0pt;font-family:"Tahoma","sans-serif"'> hw-list-bounces@list.hw.cz
[mailto:hw-list-bounces@list.hw.cz] <b>On Behalf Of </b>Pavel KREJCI<br>
<b>Sent:</b> Tuesday, December 15, 2009 10:54 AM<br>
<b>To:</b> HW-news<br>
<b>Subject:</b> Re: OT vypocet stran kvadru<o:p></o:p></span></p>
</div>
<p class=MsoNormal><o:p> </o:p></p>
<p class=MsoNormal style='margin-bottom:12.0pt'>No ale ve finale potrebujem
konkretni delky stran a tam se podle me bez kvadratu neobejdem, proto se ptam
na konkretni vysledek. <br>
Ja se v tom myslenkovem pochodu nejak zamotavam. Pro jakykoliv kvadr plati, ze
kdyz chci udelat jiny kvadr k nemu podobny, tak dostanu k*X, k*Y a k*Z na to ty
uhly znat nepotrebuju. Pro pochopeni mi tam chybi nejaka ta rovnice, zrejme
nemam takovou predstavivost ani po ranu.<br>
<br>
_Vyjadeni vzajemnych pomeru vsech stran_.<br>
Treba Y/X=tg(fi) Y/Z=tg(theta) a z toho X*tg(fi)=Z*tg(theta) ale porad nevidim
tu presmycku na k*X, k*Y a k*Z<br>
<br>
_pomer na horni strane_ X/Z = tg(theta)/tg(fi) chybi mi presmycka na k*S<br>
<br>
_zname pomer ulopricky na horni strane a vysky_ tady jsem se zasek,
protoze neznam tu uhlopricku a neznam ani uhel telesove uhlopricky (elevaci)
muzu sice napsat ze sin(elevace)=Y/R a dal pro vysku a uhlopricku Y/uXZ=tg(elevace)
ale porad mi to nedocvakava<br>
<br>
_muzeme vycislit uhel <(R;Y)_ ja "vycislim" uhel
<(R;XZ) =elevace = arcsin(Y/R)<br>
<br>
_vycislime uhlopricku_ napriklad uXZ*tg(elevace)=R*sin(elevace) =>
uXZ=R*cos(elevace) = uXZ=R*(arcsin(Y/R)) jenze Y stale neznam... jsem v koncich<br>
<br>
PK<br>
<br>
<o:p></o:p></p>
<div>
<p class=MsoNormal>2009/12/15 <<a href="mailto:jiri@bezstarosti.cz">jiri@bezstarosti.cz</a>><o:p></o:p></p>
<p class=MsoNormal>Myslel jsem tim, ze si vystacime se sinem a jeho bratry,
zadny kvadrat a<br>
ani slozity rozklad by zde vzniknout nemel. Stale zjistujeme pomer stran v<br>
pravouhlem trojuhelniku (primo vysledky goniometrickych funkci), pripadne<br>
opacne uhel z pomeru stran... No a samozrejme nasobeni a deleni, to snad<br>
neni tak moc ;).<br>
<br>
--<br>
<span style='color:#888888'>Jiri Bezstarosti</span><o:p></o:p></p>
<div>
<p class=MsoNormal><br>
<br>
> A co je vyssi matematika?<br>
> Muzem videt vysledek, jestli nahodou pouhe geometricke funkce taky nebudou<br>
> v<br>
> kvadratech pod odmocninou? ;)<br>
><br>
> PK<br>
><o:p></o:p></p>
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