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Home » From Nervous to Unstoppable: How Student Beans Dominate Every Exam - Coaching Toolbox

From Nervous to Unstoppable: How Student Beans Dominate Every Exam - Coaching Toolbox

📅 May 4, 2026 👤 scraface

May 04, 2026

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

📌 Thus, the length of the longest altitude is:

📌 Question: A climate strategist is modeling a triangular plot of land on a coast, with vertices at $ (0, 0) $, $ (6, 0) $, and $ (3, 6) $. What is the radius of the inscribed circle of this triangle?

📌 Let the triangle have vertices $ A(0, 0) $, $ B(6, 0) $, and $ C(3, 6) $. First, compute the side lengths using the distance formula:

📌 Now compute the area using the coordinate formula:

📌 Thus, the radius of the inscribed circle is:

📌 Question: A geographer models a coastal region as a triangle with side lengths $ 10 $, $ 10 $, and $ 12 $. What is the ratio of the area of the triangle to the area of its incircle?

📌 This is an isosceles triangle with sides $ a = 10

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