（2008?武清区二模）如图，在正三棱锥S-ABC中，M是侧棱SC的中点，且AB=3，SA=10，则BM与底面ABC所成的角
(2008.\u4e0a\u6d77\u4e2d\u8003\uff09\u5982\u56fe\uff0c\u5728\u4e09\u89d2\u5f62ABC\u4e2d\uff0c\u70b9D\u5728\u8fb9AC\u4e0a\uff0cDB=BC\uff0c\u70b9E\u662fCD\u7684\u4e2d\u70b9\uff0c\u70b9F\u662fAB\u7684\u4e2d\u70b9\u3002\u8bc1\u660e\uff1a1.\u8fde\u63a5BE.\u7531\u4e8eBD=BC,DE=CE\u6240\u4ee5BE\u22a5AC,\u53c8BF=AF,\u6240\u4ee5\uff0cEF=2\u5206\u4e4b1AB
2.AG\u2016EF,\u6240\u4ee5\uff0c\u2220FEB=\u2220AGE,\u800cEF=2\u5206\u4e4b1AB\uff0c\u6240\u4ee5\u2220FEB=\u2220ABC.\u56e0\u4e3aBE\u22a5AC\uff0c\u6240\u4ee5\u25b3ABE\u224c\u25b3AGE.
\u6211\u7701\u4e86\u4e00\u4e9b\u6b65\u9aa4\uff0c\u4e0d\u8fc7\u6211\u76f8\u4fe1\u4f60\u662f\u53ef\u4ee5\u770b\u7684\u61c2\u5f97\u3002
\u5982\u56fe1\uff0c\u5728\u25b3ABC\u4e2d\uff0c\u70b9P\u4e3aBC\u8fb9\u4e2d\u70b9\uff0c\u76f4\u7ebfa\u7ed5\u9876\u70b9A\u65cb\u8f6c\uff0c\u82e5B\u3001P\u5728\u76f4\u7ebfa\u7684\u5f02\u4fa7\uff0cBM\u22a5\u76f4\u7ebfa\u4e8e\u70b9M\uff0cCN\u22a5\u76f4\u7ebfa\u4e8e\u70b9N\uff0c\u8fde\u63a5PM\u3001PN\uff1b
(1) \u5ef6\u957fMP\u4ea4CN\u4e8e\u70b9E(\u5982\u56fe2)\u3002j \u6c42\u8bc1\uff1a\u25b3BPM@\u25b3CPE\uff1bk\u6c42\u8bc1\uff1aPM = PN \uff1b
(2) \u82e5\u76f4\u7ebfa\u7ed5\u70b9A\u65cb\u8f6c\u5230\u56fe3\u7684\u4f4d\u7f6e\u65f6\uff0c\u70b9B\u3001P\u5728\u76f4\u7ebfa\u7684\u540c\u4fa7\uff0c\u5176\u5b83\u6761\u4ef6\u4e0d\u53d8\u3002\u6b64\u65f6PM=PN\u8fd8\u6210\u7acb\u5417\uff1f\u82e5\u6210\u7acb\uff0c\u8bf7\u7ed9\u4e88\u8bc1\u660e\uff1b\u82e5\u4e0d\u6210\u7acb\uff0c\u8bf7\u8bf4\u660e\u7406\u7531\uff1b
(3) \u82e5\u76f4\u7ebfa\u7ed5\u70b9A\u65cb\u8f6c\u5230\u4e0eBC\u8fb9\u5e73\u884c\u7684\u4f4d\u7f6e\u65f6\uff0c\u5176\u5b83\u6761\u4ef6\u4e0d\u53d8\u3002\u8bf7\u76f4\u63a5\u5224\u65ad\u56db\u8fb9\u5f62MBCN\u7684\u5f62\u72b6\u53ca\u6b64\u65f6PM=PN\u8fd8\u6210\u7acb\u5417\uff1f\u4e0d\u5fc5\u8bf4\u660e\u7406\u7531\u3002
\u7b54\u6848\uff1a
(1) \u8bc1\u660e\uff1aj \u5982\u56fe2\uff0c\u2235BM\u22a5\u76f4\u7ebfa\u4e8e\u70b9M\uff0cCN\u22a5\u76f4\u7ebfa\u4e8e\u70b9N\uff0c
\u2234ÐBMN=ÐCNM=90\u00b0\uff0c\u2234BM//CN\uff0c\u2234ÐMBP=ÐECP\uff0c
\u53c8\u2235P\u4e3aBC\u8fb9\u4e2d\u70b9\uff0c\u2234BP=CP\uff0c\u53c8\u2235ÐBPM=ÐCPE\uff0c\u2234\u25b3BPM@\u25b3CPE\uff0c
k \u2235\u25b3BPM@\u25b3CPE\uff0c\u2234PM=PE\uff0c\u2234PM=1/2 ME\uff0c\u2234\u5728Rt\u25b3MNE\u4e2d\uff0cPN=1/2 ME\uff0c
\u2234PM=PN\uff1b
(2) \u6210\u7acb\uff0c\u5982\u56fe3\uff0c
\u8bc1\u660e \u5ef6\u957fMP\u4e0eNC\u7684\u5ef6\u957f\u7ebf\u76f8\u4ea4\u4e8e\u70b9E\uff0c\u2235BM^\u76f4\u7ebfa\u4e8e\u70b9M\uff0cCN^\u76f4\u7ebfa\u4e8e\u70b9N\uff0c
\u2234ÐBMN=ÐCNM=90\u00b0\uff0c\u2234ÐBMN+ÐCNM=180\u00b0\uff0c\u2234BM//CN\uff0c\u2234ÐMBP=ÐECP\uff0c
\u53c8\u2235P\u4e3aBC\u4e2d\u70b9\uff0c\u2234BP=CP\uff0c\u53c8\u2235ÐBPM=ÐCPE\uff0c\u2234\u25b3BPM@\u25b3CPE\uff0c\u2234PM=PE\uff0c
\u2234PM=1/2 ME\uff0c\u5219\u5728Rt\u25b3MNE\u4e2d\uff0cPN=1/2 ME\uff0c\u2234PM=PN\u3002
(3) \u56db\u8fb9\u5f62MBCN\u662f\u77e9\u5f62\uff0cPM=PN\u6210\u7acb\u3002
\u7ee7\u7eed\u8ffd\u95ee\uff1a \u7b2c\u4e09\u4e2a\u95ee\u7684\u7406\u7531\u80fd\u7ed9\u6211\u5417\uff1f\u8c22\u8c22 \u8865\u5145\u56de\u7b54\uff1a
\u5982\u56fe4\uff0c\u2235BM\u22a5\u76f4\u7ebfa\u4e8e\u70b9M\uff0cCN\u22a5\u76f4\u7ebfa\u4e8e\u70b9N\uff0cMN//BC \uff0c
\u2234BM=CN
\u53c8\u2235P\u4e3aBC\u8fb9\u4e2d\u70b9\uff0c\u2234BP=CP\uff0c\u2234\u25b3BPM@\u25b3CPE\uff0c
\u2234PM=PN\u3002
过M作MF⊥平面ABC，交AE于F，
∵在正三棱锥S-ABC中，M是侧棱SC的中点，且AB=3，SA=
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