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今年高考理科数学第四题是立几计算题:“如图,设平面AC和BD相交于BC,它们所成的一个二面角为45°,P为面AC内的一点,Q为面BD内的一点。已知直线MQ是直线PQ在平面BD内的射影,并且M在BC上。又设PQ与平面BD所成的角为β,∠CMQ=θ(0°<θ<90°),线段PM的长为a。求线段PQ的长。”这题主要是考查立几中斜线在平面内的射影、二面角及其平面角、斜线与平面所成的角等重要概念和三垂线定理,考查空间图形的想象能力和综合运用知识的能力。这道试题实际是以课本第42页的例题为基础,加进斜线在平面内的射影、斜线与平面所成的角两个概念后略加变
This year's college entrance examination science mathematics fourth question is to set a few calculations: “As shown, set the plane AC and BD intersection in BC, they formed a dihedral angle of 45 °, P is the surface AC within a point, Q is the surface BD It is known that the straight line MQ is the projection of the straight line PQ in plane BD and M is on BC, and the angle formed by PQ and plane BD is β, ∠CMQ = θ (0 ° <θ <90 °) , The length of the line segment PM is a. Find the length of the line segment PQ. ”This question mainly examines important concepts such as the projection of the slanted line in the plane, the dihedral angle and its plane angle, and the angle formed by the slanted line and the plane And the three perpendicular theorem, examine the imagination of spatial graphics and the ability to comprehensively use knowledge. This question is actually based on the example of the textbook on page 42, adding a slash in the plane of the projective, slash and the angle of the plane formed by the two slightly modified