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Home » The Most Common Reason Your Nose Piercing Hurts… And How to Fix It Fast! - AMAZONAWS

The Most Common Reason Your Nose Piercing Hurts… And How to Fix It Fast! - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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📌 \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.

📌 Die Fläche eines Dreiecks ist gegeben durch \(\frac{1}{2} \cdot \text{Basis} \cdot \text{Höhe}\). Für das ursprüngliche Dreieck ist die Basis 10 cm und sei \(h\) die Höhe vom Scheitel zwischen den Basisecken. Dann:

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