## vf321 2 years ago For a given triangle ABC, where $$h_X$$ stands for altitude from a vertex $$X$$, is $$h_b+h_c>b$$ for all $$b$$?

1. vf321

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2. vf321

$h_c = a \sin B$$h_b = c \sin A$$b^2 = a^2+c^2-2a c\cos B$$b^2\sin^2 A \sin^2 B=h_c^2\sin^2 A+h_b^2\sin^2B-2h_ch_b \cos B \sin B\sin A$