求助，做立体几何题，建立坐标系的时候，给的图形是正三棱柱， 底面是等边三角形，我这时候怎么建立x， 这是一道高中立体几何证明题，请看图片上的问题？
\u4e00\u4e2a\u9ad8\u4e2d\u6570\u5b66\u7acb\u4f53\u51e0\u4f55\u4ee5C\u4e3a\u539f\u70b9 CB\u4e3ay ,CC1\u4e3aZ\u8f74\uff0c\u5e73\u9762ABC\u5185\u8fc7C\u4f5cCB\u7684\u5782\u7ebf\u4e3ax\u8f74\uff0c\u5efa\u7acb\u7a7a\u95f4\u76f4\u89d2\u5750\u6807\u7cfb\uff0c
\u8bbe\u5e95\u9762\u4e09\u89d2\u5f62\u7684\u8fb9\u957f\u4e3aa\uff0c
\u8fc7A\u4f5cx\u8f74\u7684\u5782\u7ebf\uff0c\u5782\u8db3\u4e3aM\uff0cAM=a/2\uff0cCM=\u221a3a/2 \uff08\u5efa\u8bae\u753b\u5e73\u9762\u76f4\u89d2\u5750\u6807\u7cfb\uff0cC\u4e3a\u539f\u70b9 CB\u4e3ay \uff0c
\u25b3ABC\u4e3a\u7b49\u8fb9\u4e09\u89d2\u5f62\uff0c\u8fd9\u6837\u5c31\u5bb9\u6613\u6c42\u51faA\u7684\u5750\u6807\uff09
D\u662fAC\u7684\u4e2d\u70b9\uff0c\u4e2d\u70b9\u5750\u6807\u516c\u5f0f\uff0cC\uff080,0,0\uff09
A\u70b9\u5750\u6807\u51fa\u6765\uff0cD\u5c31\u597d\u6c42\u4e86
\u7b54\uff1a\u5148\u56de\u7b54\u4f60\u63d0\u7684\u95ee\u9898\uff0c\u4f60\u628a\u76f4\u68f1\u67f1\u7684\u5173\u7cfb\u7528\u53cd\u4e86\uff0c\u5e94\u8be5\u662f\u4fa7\u68f1\u22a5(\u4e0a\u3001\u4e0b)\u5e95\u9762\uff0c\u800c\u4e0d\u4e00\u5b9a\u662f\u5e95\u8fb9\u22a5\u4fa7\u68f1\uff1b\u53ea\u6709\u5e95\u9762\u4e3a\u76f4\u89d2\u4e09\u89d2\u5f62\u65f6,\u624d\u53ef\u4ee5\u8fd0\u7528\u4f60\u7684\u65b9\u6cd5;\u800c\u9898\u9762\u7684\u5df2\u77e5\u6761\u4ef6\u6ca1\u6709\u660e\u786e\u8bf4\u660e\u5e95\u9762\u662f\u76f4\u89d2\u4e09\u89d2\u5f62\u4e4b\u524d\uff0c\u662f\u4e0d\u53ef\u4ee5\u4eba\u4e3a\u5b9a\u4e49\u4e3a\u76f4\u89d2\u4e09\u89d2\u5f62\u7684\uff0c\u6240\u4ee5\uff0c\u4f60\u7684\u65b9\u6cd5\u4e0d\u53ef\u4ee5\u7528\u3002\u8fd9\u6837\u8bc1\u660e\u8fdd\u53cd\u903b\u8f91\u5173\u7cfb\u3002
\u8bc1\u660e\uff1a\u89c1\u4e0b\u56fe,\u56fe\u4e2d\u9ed1\u8272\u7ebf\u4e3a\u5b9e\u7ebf\uff0c\u7ea2\u8272\u7ebf\u4e3a\u539f\u56fe\u4e2d\u7684\u865a\u7ebf\uff0c\u84dd\u8272\u7ebf\u4e3a\u8f85\u52a9\u7ebf\u3002
(1)\u56e0\u4e3aAC=4, AB=5,cos\u2220CAB=4/5=AC/AB, \u6240\u4ee5AB\u8fb9\u6240\u5bf9\u7684\u2220ACB\u662f\u76f4\u89d2\uff0c\u6240\u4ee5AC\u22a5BC\uff1b\u56e0\u4e3a\u4e09\u68f1\u67f1ABC-A1B1C1\u662f\u76f4\u4e09\u68f1\u67f1\uff0c\u6240\u4ee5C1C\u22a5\u5e73\u9762ABC\uff0cC1C\u22a5AC (AC\u2208\u9762ABC)\uff0c\u6240\u4ee5AC\u22a5\u5e73\u9762BB1C1C\uff08AC\u22a5\u5e73\u9762BB1C1C\u5185\u7684\u4e24\u6761\u76f8\u4ea4\u76f4\u7ebf),\u6240\u4ee5\uff0cAC\u22a5BC1\u3002
(2)\u8bbeB1C\u548cBC1\u76f8\u4ea4\u4e8eE\uff0c\u8fde\u7ed3DE\uff0c\u56e0\u4e3aBB1C1C\u662f\u77e9\u5f62\uff0c\u6240\u4ee5E\u662fBC1\u7684\u4e2d\u70b9\uff0c\u800cD\u662fAB\u7684\u4e2d\u70b9\uff0c\u6240\u4ee5DE\u662f\u25b3BC1A\u4e2dAC1\u8fb9\u7684\u4e2d\u4f4d\u7ebf\uff0c\u6240\u4ee5AC1//DE\uff0cDE\u2208\u5e73\u9762CDB1\uff0c\u6240\u4ee5AC1//\u5e73\u9762CDB1\u3002
\uff083\uff09\u8bf7\u770b6\u9762\u4f53\u56fe\u5f62\u3002\u628a\u56db\u9762\u4f53A1-CDB1\u6269\u5927\u4e00\u500d\u5230A1-CPB1\uff0c\u6839\u636e\u52fe\u80a1\u5b9a\u7406\u5b9a\u7406BC=3\uff0c\u56e0\u4e3aAA1=3\uff0c\u6240\u4ee5A1APP1\u662f\u6b63\u65b9\u5f62\uff0c\u5219\u5bf9\u89d2\u7ebfA1P=B1C=3\u221a3\uff0cA1B1=B1P=A1C=CP=5\uff1b\u4f5cCF\u22a5A1P\u4e8eF\uff0c\u8fde\u7ed3B1F\uff0c\u56e0\u4e3aF\u662fA1P\u8fb9\u7684\u4e2d\u70b9\uff0c\u6240\u4ee5B1F\u22a5A1P\uff0c\u2220CFB1\u4e3a\u5e73\u9762B1CP\u548c\u5e73\u9762CA1P\u7684\u4e8c\u9762\u89d2\u3002CF=B1F=\u221a[5^2-(3\u221a2)^2=\u221a25-9/2=\u221a(59/2); \u6839\u636e\u4f59\u5f26\u5b9a\u7406\uff1a
cos\u2220CFB1=[2*59/2-(3\u221a2)^]/(2*59/2)=41/59, sin\u2220CFB1=\u221a1-(41/59)^2=\u221a(18/59);
VA1-CDB1=(1/3)A1F*B1F*CF*sin\u2220CFB1=(1/3)(3\u221a2)(59/2)*\u221a(18/59)=3\u221a59\u3002
或者一个顶点设为原点，一条边为x轴
这两种建立的方式比较多也好算
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