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Home » 2; Dock Spider Secrets: How This Tiny Gadget Saves Time and Fishing Success! - Treasure Valley Movers

2; Dock Spider Secrets: How This Tiny Gadget Saves Time and Fishing Success! - Treasure Valley Movers

📅 April 17, 2026 👤 scraface

Apr 17, 2026

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📌 Let $a = 45^\circ$, $b = 30^\circ$, so:

📌 \tan 75^\circ = \tan(45^\circ + 30^\circ) = \frac{\tan 45^\circ + \tan 30^\circ}{1 - \tan 45^\circ \tan 30^\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}

📌 Multiply numerator and denominator by $\sqrt{3} + 1$:

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

📌 \boxed{2 + \sqrt{3}}

📌 Question: A historian discovers a triangular tablet with sides 17 cm, 25 cm, and 28 cm. What is the radius of the circumscribed circle around the triangle?

📌 Solution: Use the formula for the circumradius $R$ of a triangle:

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