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canis lupus canis familiaris - Deep Underground Poetry

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 \frac{1}{2} \cdot 10 \cdot h = 45 \Rightarrow 5h = 45 \Rightarrow h = 9.

📌 Somit beträgt die Höhe des gleichschenkligen Dreiecks \(\boxed{9}\) cm.

📌 Frage: Die Länge der Hypotenuse eines rechtwinkligen Dreiecks beträgt \(13\) cm, und eine Kathete ist \(5\) cm lang. Wenn ein Kreis in das Dreieck eingeschrieben ist, wie groß ist der Radius des Kreises?

📌 Gegeben ist ein rechtwinkliges Dreieck mit Hypotenuse \(c = 13\) cm und einer Kathete \(a = 5\) cm. Zuerst die andere Kathete \(b\) mit dem Satz des Pythagoras finden:

📌 b = \sqrt{c^2 - a^2} = \sqrt{13^2 - 5^2} = \sqrt{169 - 25} = \sqrt{144} = 12 \text{ cm}.

📌 Der Radius \(r\) des eingeschriebenen Kreises in einem rechtwinkligen Dreieck ist gegeben durch:

📌 r = \frac{a + b - c}{2} = \frac{5 + 12 - 13}{2} = \frac{4}{2} = 2 \text{ cm}.

📌 Somit beträgt der Radius des eingeschriebenen Kreises \(\boxed{2}\) cm.

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