Question

已知：RT三角形ABC中，∠C=90°，AC=4，cotB=根号3，MN=2，QM垂直于AB

已知：RT三角形ABC中，∠C=90°，AC=4，cotB=根号3，MN=2，QM垂直于AB，PN平行于QM，设AM=x，MNPO的面积为y
1) 当X=5/6时，球PB的长
2）求y关于x 的函数解析式，并写出X的取值范围。
3）三角形PCQ与三角形QMA能相似吗？若能，请写出X的值，若不能，请说明理由
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Answer 1

cotB=根3，所以B=30°，所以AB=AC/sin30°=8，所以BN=AB-AN=31/6，所以PB=BN/cos30,=31根3/9
QM=tan60X，PN=（8-X-2）tan30，所以带入梯形面积公式，y=2根3/3X+2根3，0≤X≤6
假设其相似，则Q一定在AC边上，所以∠A=∠CPQ=60°，所以AQ=2X，QC=4-2X，过Q作QE垂直PN，则MN=QE=2，且，∠PQE=30°，所以PQ=4/根3，所以由三角形相似，PQ/AQ=QC/QM
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Answer 2

第一问，cotB=根3，所以B=30°，所以AB=AC/sin30°=8，所以BN=AB-AN=31/6，所以PB=BN/cos30,=31根3/9
第二问，QM=tan60X，PN=（8-X-2）tan30，所以带入梯形面积公式，y=2根3/3X+2根3，0≤X≤6
第三问，假设其相似，则Q一定在AC边上，所以∠A=∠CPQ=60°，所以AQ=2X，QC=4-2X，过Q作QE垂直PN，则MN=QE=2，且，∠PQE=30°，所以PQ=4/根3，所以由三角形相似，PQ/AQ=QC/QM，所以带入数据我自己随便算了下，两个X都是负值，应该不存在这样的X吧，具体应该是这样写，答案你在自己算算吧，我不确定~谢谢哈~打字好麻烦，打了好长时间呢~

Answer 3

第一问，cotB=根3，所以B=30°，所以AB=AC/sin30°=8，所以BN=AB-AN=31/6，所以PB=BN/cos30,=31根3/9
第二问，QM=tan60X，PN=（8-X-2）tan30，所以带入梯形面积公式，y=2根3/3X+2根3，0≤X≤6
第三问，假设其相似，则Q一定在AC边上，所以∠A=∠CPQ=60°，所以AQ=2X，QC=4-2X，过Q作QE垂直PN，则MN=QE=2，且，∠PQE=30°，所以PQ=4/根3，所以由三角形相似，PQ/AQ=QC/QM，所以带入数据我自己随便算了下，两个X都是负值，应该不存在这样的X吧，具体应该是这样写，答案你在自己算算吧，我不确定~谢谢哈~打字好麻烦，打了好长时间呢~