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“时代杯”2013年江苏省中学数学应用与创新邀请赛(初中组)有这样一道试题:图1题目如图1,在△ABC中,∠ACB=120°,点D在AB上,且AD∶DB=3∶2,AC⊥CD,则tanA等于().(A)25(B)35(C)2槡35(D)3槡35分析本题题干短小,条件清晰,构图简单,是一道融平面几何与三角知识为一体的综合性试题.已知条件中的∠ACB=120°及AC⊥CD为习题中所常见,而条件AD∶DB=3∶2的运用往往较为棘手.注意到所求的是tanA的值,实质就是求两条线段的比值,因此能否合理利用AD∶DB=3∶2这一条件是本
“Era Cup ” 2013 Jiangsu province high school mathematics application and innovation invitational (junior high school group) has such a test: Figure 1 title as shown in Figure 1, △ ABC, ∠ ACB = 120 °, the point D in the AB, and (A) 25 (B) 35 (C) 2 槡 35 (D) 3 槡 35 Analysis of the title dry short, the conditions are clear, the composition is simple, Is a comprehensive test that integrates planar geometry and trigonometric knowledge.It is often tricky to use ∠ACB = 120 ° and AC⊥CD in the known conditions, and the condition AD: DB = 3: 2. Note that the value of tanA is obtained, the essence is to find the ratio of two line segments, so the reasonable use of AD: DB = 3: 2 this condition is the