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doubletree suites by hilton hotel raleigh durham durham nc - Deep Underground Poetry

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 Question: Compute $\tan 45^\circ + \sin 315^\circ$.

📌 Solution: $\tan 45^\circ = 1$. $\sin 315^\circ = \sin(360^\circ - 45^\circ) = -\sin 45^\circ = -\frac{\sqrt{2}}{2}$. Therefore, the expression becomes:

📌 + \left(-\frac{\sqrt{2}}{2}\right) = 1 - \frac{\sqrt{2}}{2}

📌 \boxed{1 - \frac{\sqrt{2}}{2}}

📌 Question: Find the length of the shortest altitude of a triangle with side lengths 13 cm, 14 cm, and 15 cm.

📌 Solution: First, compute the area using Heron’s formula. The semi-perimeter is:

📌 s = \frac{13 + 14 + 15}{2} = 21

📌 A = \sqrt{21(21 - 13)(21 - 14)(21 - 15)} = \sqrt{21 \cdot 8 \cdot 7 \cdot 6} = \sqrt{7056} = 84

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