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In △ ABC, if Sina: SINB: sinc = 2:3:4, then the cosine value of the largest angle=______ ．
In ∵ △ ABC, Sina: SINB: sinc = 2:3:4, according to the sine theorem, we can get a: B: C = 2:3:4, we can get C as the largest edge, angle c is the largest angle, let a = 2K, B = 3k, C = 3K (k > 0) ∵ COSC = A2 + B2 − c22ab = 4k2 + 9k2 − 16k22 × 2K × 3K = - 14, that is, the cosine value of the largest angle is - 14, so the answer is: - 14
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