====== Der Satz des Pythagoras ======

Dieser Artikel kann als {{:stud:basismathe:satz_des_pythagoras.pdf|PDF-Fassung}} heruntergeladen werden.
===== Rechtwinkliges Dreieck =====

{{:stud:basismathe:pythadreieck.png?nolink|Rechtwinkliges Dreieck}}
===== Formeln =====

Für eine **Hypothenuse** {{http://apps.rkcsd.com/latex2png.php/c.png?nolink|c}} und die **Katheten** {{http://apps.rkcsd.com/latex2png.php/a.png?nolink|a}} und {{http://apps.rkcsd.com/latex2png.php/b.png?nolink|b}} gilt im **rechtwinkligen Dreieck** der **Satz des Pythagoras**: {{http://apps.rkcsd.com/latex2png.php/a%5E2+b%5E2=c%5E2.png?nolink|a^2+b^2=c^2}}\\

Umformungen:\\
{{http://apps.rkcsd.com/latex2png.php/c%5E2-b%5E2=a%5E2.png?nolink|c^2-b^2=a^2}}\\
{{http://apps.rkcsd.com/latex2png.php/c%5E2-a%5E2=b%5E2.png?nolink|c^2-a^2=b^2}}\\

Zum direkten Ausrechnen:\\
{{http://apps.rkcsd.com/latex2png.php/c=%5Csqrt%7Ba%5E2+b%5E2%7D.png?nolink|c=\sqrt<a^2+b^2>}}\\
{{http://apps.rkcsd.com/latex2png.php/a=%5Csqrt%7Bc%5E2-b%5E2%7D.png?nolink|a=\sqrt<c^2-b^2>}}\\
{{http://apps.rkcsd.com/latex2png.php/b=%5Csqrt%7Bc%5E2-a%5E2%7D.png?nolink|b=\sqrt{c^2-a^2}}\\

Hypothenusenabschnitt {{http://apps.rkcsd.com/latex2png.php/p.png?nolink|p}}: {{http://apps.rkcsd.com/latex2png.php/p=%28a%5E2%29%5Cdiv%20c.png?nolink|p=(a^2)\div c}}\\
Hypothenusenabschnitt {{http://apps.rkcsd.com/latex2png.php/q.png?nolink|q}}: {{http://apps.rkcsd.com/latex2png.php/q=%28b%5E2%29%20%5Cdiv%20c.png?nolink|q=(b^2) \div c}}\\

Höhe {{http://apps.rkcsd.com/latex2png.php/h.png?nolink|h}}: {{http://apps.rkcsd.com/latex2png.php/h=%5Csqrt%7Bp%5Ctimes%20q%7D.png?nolink|h=\sqrt<p\times q>}}\\
Umfang {{http://apps.rkcsd.com/latex2png.php/U.png?nolink|U}}: {{http://apps.rkcsd.com/latex2png.php/U=a+b+c.png?nolink|U=a+b+c}}\\
Flächeninhalt {{http://apps.rkcsd.com/latex2png.php/A.png?nolink|A}}: {{http://apps.rkcsd.com/latex2png.php/A=%28a%5Ctimes%20b%29%20%5Cdiv%202.png?nolink|A=(a\times b) \div 2}}

Winkel:\\
{{http://apps.rkcsd.com/latex2png.php/%5Calpha%20=%20%5Carccos%28%28b%5E2+c%5E2-a%5E2%29%20%5Cdiv%202bc%29.png?nolink|\alpha = \arccos((b^2+c^2-a^2) \div 2bc)}}\\
{{http://apps.rkcsd.com/latex2png.php/%5Cbeta%20=%20%5Carccos%28%28a%5E2+c%5E2-b%5E2%29%20%5Cdiv%202bc%29.png?nolink|\beta = \arccos((a^2+c^2-b^2) \div 2bc)}}\\
{{http://apps.rkcsd.com/latex2png.php/%5Cgamma=90%5E%5Ccirc.png?nolink|\gamma=90^\circ}}