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87年高考试卷理工类第四题是: 如图,三棱锥P-ABC中,已知PA(?)BC,PA=BC=l,PA、BC的公垂线ED=h,求证三棱锥P-ABC的体积V=1/6b~2h这是一道由已知三棱锥的一组对棱的长以及它们的相对位置(所成的角和距离)计算其体积的问题。如果使问题一般化,即令对棱PA、BC所成角为α,则有下列关于三棱锥体积的一个定理。定理三棱锥的一组对棱长分别为a、b,它们的距离和所成的角分别为h、a,则三棱锥体积V=1/6abhsinα。
The fourth issue of the 87-year high exam paper is: As shown in the figure, in the triangular pyramid P-ABC, PA(?)BC, PA=BC=l, and the vertical line of PA, BC=ED, confirming the triangular pyramid P - Volume of ABC V = 1/6b~2h This is a problem of calculating the volume of a pair of diagonals of known triangular pyramids and their relative positions (angles and distances formed). If the problem is generalized, even if the angle formed by the pair of edges PA, BC is α, then there is a theorem about the volume of the triangular pyramid. The length of a set of paired prisms of the theorem of a theorem is a and b, respectively. Their distances and angles formed are h and a, respectively, and the volume of the triangular pyramid is V=1/6abhsinα.