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In the first paragraph under “Deriving lengths of the sides of the smaller triangle”, how do we know the length of the third side is 2a^2/b ?


"This" in "This leads to the third side of this triangle to be 2a²/b." means "the same line of reasoning".

it's not even trigonometry in that paragraph, just rudimentary proportions of similar triangles


From cosβ = a/c and cosβ = third side/((2ac)/b)




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