設(shè)
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是銳角三角形,
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分別是內(nèi)角
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所對邊長,并且
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.
(1)求角

的值;
(2)若

,求
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(其中

).
(1)
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;(2)
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.
試題分析:(1) 利用兩角和與差的正弦公式展開化簡得
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,又
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為銳角,所以
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;(2)由

可得
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,即

,然后利用余弦定理
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得
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的另一個關(guān)系,從而解出
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.
試題解析:(1)因為
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

,
所以
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,又
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為銳角,所以

.
(2)由

可得
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①
由(1)知

,所以

②
由余弦定理知

,將
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及①代入,得
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③
③+②×2,得

,所以

因此,
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是一元二次方程

的兩個根.
解此方程并由

知
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.
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
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
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
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
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
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
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