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由于线面距离及面面距离常转化为点面距离来求,异面直线的距离有时也转化为线面距离,进而转化为点面距离求解,所以点面距离的求法是学习的重点,学生必须掌握. 一、定义法构造垂面,利用面面垂直性质作出点面距离来求. 例1 (1993年上海高考题24题改编)已知二面角α-PQ-β为60°,点A和B分别在平面α和平面β上,点C在棱PQ上,∠ACP=∠BCP=30°,CA=CB=a,求点B到平面α的距离.
Since the line distance and face distance are often converted into point distances, the distances of the different straight lines are sometimes converted into line distances, which are then converted into point distances. Therefore, the point distance method is the focus of study. Must be mastered. First, the definition of the law structure vertical surface, the use of facial vertical properties to make the distance point to find. Example 1 (1993 Shanghai college entrance examination questions adapted from 24 questions) known dihedral angle α-PQ-β is 60 °, point A and B are respectively on plane α and plane β, point C on edge PQ, ∠ACP=∠BCP=30°, and CA=CB=a, and the distance from point B to plane α is calculated.