A Weighted Orthocenter

★ 7/10plane geometry trigonometry Trigonometric Identities Triangle Geometry vectors

Problem

Let $H$ be the orthocenter of $\triangle ABC$ , and

3\overrightarrow{HA} + 4\overrightarrow{HB} + 5\overrightarrow{HC} = \vec 0.

Find $\cos\angle AHB$ .

Answer

Solution

Difficulty	7/10
Topics	plane geometry, trigonometry, Trigonometric Identities, Triangle Geometry, vectors

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