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如圖,正三棱柱
ABC-
A1B1C1的底面邊長是2,
D是側(cè)棱
CC1的中點(diǎn),直線
AD與側(cè)面
BB1C1C所成的角為45°.
小題1:求此正三棱柱的側(cè)棱長;
小題2:求二面角
A-BD-C的大��;
小題3:求點(diǎn)
C到平面
ABD的距離.
小題1:設(shè)正三棱柱
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—

的側(cè)棱長為
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.取
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中點(diǎn)
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,連
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.
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
是正三角形,

.
又底面
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側(cè)面
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,且交線為
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.
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側(cè)面
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.
連
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,則直線
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與側(cè)面
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所成的角
為
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.
在
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中,
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,解得
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.
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此正三棱柱的側(cè)棱長為
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. ……………………5分
注:也可用向量法求側(cè)棱長.
小題2:
過
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作
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于
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,連
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,
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側(cè)面
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.
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為二面角

的平面角.
在
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中,
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,又
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,
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
.
又
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
在
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中,
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.
故二面角

的大小為

小題3:
由(Ⅱ)可知,

平面
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,
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平面

平面

,且交線為
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,
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過
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作
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于
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,則

平面

.
在
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中,
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.
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
為
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中點(diǎn),
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點(diǎn)
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到平面

的距離為
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. …………14分
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
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
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
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
平面

;
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
為線段
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
,問
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為何值時能使
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
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
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