(本題滿分14分)
已知△
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中,
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在邊
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上,且
o,
o.
(1)求
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的長;
(2)求△
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的面積.
(1)
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;(2)
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.
第一問中利用內(nèi)角和定理,在△ABC中,∠BAD=150
o-60
o=90
o,∴AD=2sin60
o=
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.
在△ACD中,AD
2=(
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)
2+1
2-2×
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×1×cos150
o=7,∴AC=
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第二問∴AB=2cos60
o=1.S
△ABC=
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×1×3×sin60
o=
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解:在△ABC中,∠BAD=150
o-60
o=90
o,∴AD=2sin60
o=
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.……… 4分
在△ACD中,AD
2=(
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)
2+1
2-2×
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×1×cos150
o=7,∴AC=
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.…… 10分
∴AB=2cos60
o=1.S
△ABC=
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×1×3×sin60
o=
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. ………… 14分
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