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Home » Is Onii Chan Chan the Mysterious Figure Ruining Your Day? Here’s the Truth! - Simpleprint

Is Onii Chan Chan the Mysterious Figure Ruining Your Day? Here’s the Truth! - Simpleprint

📅 March 13, 2026 👤 scraface

Mar 13, 2026

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📌 Wir wissen, dass \(\tan 45^\circ = 1\) und \(\tan 30^\circ = \frac{1}{\sqrt{3}}\). Einsetzen:

📌 \tan 75^\circ = \frac{1 + \frac{1}{\sqrt{3}}}{1 - 1 \cdot \frac{1}{\sqrt{3}}} = \frac{\frac{\sqrt{3} + 1}{\sqrt{3}}}{\frac{\sqrt{3} - 1}{\sqrt{3}}} = \frac{\sqrt{3} + 1}{\sqrt{3} - 1}.

📌 Rationalisieren des Nenners:

📌 \frac{\sqrt{3} + 1}{\sqrt{3} - 1} \cdot \frac{\sqrt{3} + 1}{\sqrt{3} + 1} = \frac{(\sqrt{3} + 1)^2}{(\sqrt{3})^2 - (1)^2} = \frac{3 + 2\sqrt{3} + 1}{3 - 1} = \frac{4 + 2\sqrt{3}}{2} = 2 + \sqrt{3}.

📌 Somit ist \(\tan 75^\circ = \boxed{2 + \sqrt{3}}\).

📌 Frage: Ein gleichschenkliges Dreieck hat eine Basis von 10 cm und neue Höhen, die von den Basisecken zum gegenüberliegenden Scheitelpunkt gezogen werden, wodurch es in drei kleinere Dreiecke unterteilt wird. Wenn jede der neuen Dreiecke eine Fläche von 15 cm² hat, wie lang ist die Höhe des ursprünglichen gleichschenkligen Dreiecks?

📌 Das ursprüngliche gleichschenklige Dreieck wird durch zwei Höhen, jeweils von den Basisecken zum Scheitelpunkt, in drei kleinere Dreiecke unterteilt. Jedes dieser hat eine Fläche von 15 cm², sodass die Gesamtfläche des Dreiecks beträgt:

📌 \times 15 = 45 \text{ cm}^2.

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