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Home » \[ x = -\fracb2a. \] - go-checkin.com

\[ x = -\fracb2a. \] - go-checkin.com

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 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

📌 The altitude corresponding to side $a$ is given by $h_a = \frac{2A}{a}$. Compute each altitude:

📌 h_{13} = \frac{2 \cdot 84}{13} = \frac{168}{13}, \quad h_{14} = \frac{168}{14} = 12, \quad h_{15} = \frac{168}{15} = 11.2

📌 The shortest altitude is $11.2$.

📌 Question: Compute $\cos 180^\circ + \cot 30^\circ$.

📌 Solution: $\cos 180^\circ = -1$, and $\cot 30^\circ = \frac{1}{\tan 30^\circ} = \frac{1}{\frac{\sqrt{3}}{3}} = \sqrt{3}$. Therefore:

📌 \cos 180^\circ + \cot 30^\circ = -1 + \sqrt{3}

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