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📅 May 1, 2026 👤 scraface

May 01, 2026

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📌 The arc length $ s $ of a circular sector is given by the formula:

📌 Now, the area $ A $ of a circular sector is given by:

📌 Thus, the area of the circular sector is:

📌 Question: An aerospace engineer is analyzing the trajectory of a rocket modeled as a triangle with side lengths $ 13 $, $ 14 $, and $ 15 $ kilometers. What is the length of the longest altitude of this triangle?

📌 Let the triangle have sides $ a = 13 $, $ b = 14 $, and $ c = 15 $. The longest altitude corresponds to the shortest side, which is $ a = 13 $, because the altitude is inversely proportional to the base.

📌 First, compute the area using Herons formula. The semi-perimeter $ s $ is:

📌 Now, the altitude $ h $ corresponding to side $ a = 13 $ is given by:

📌 Thus, the length of the longest altitude is:

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