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1试题及参考答案题目:如图1,在同一平面内,两条平行高速公路l_1和l_2间有一条“Z”型道路连通,其中AB段与高速公路l_1成30°,长为20 km;BC段与AB、CD段都垂直,长为10 km;CD段长为30 km,求两高速公路间的距离。(结果保留根号)(2014年安徽省中考数学题)参考答案:如图2,过点A作AB的垂线交DC延长线于点E,过点E作l_1的垂线与l_1、l_2分别交于点H、F,则HF⊥l_2。由题意知AB⊥BC,BC⊥CD,又AE⊥AB,所以四边形ABCE为矩形,AE=BC,AB=EC,所以DE=DC+CE=DC+AB=50。又AB与l_1成30°角,所以∠EDF=30°,∠EAH=60°。
1 questions and reference answers subject: Figure 1, in the same plane, the two parallel highway l_1 and l_2 between a “z ” type of road connectivity, abc and highway l_1 into 30 °, length 20 km. The BC section is perpendicular to the AB and CD sections and is 10 km long. The CD section length is 30 km and the distance between two freeways is calculated. (Results retained root number) (Anhui Province in 2014 math test questions) Reference answer: As shown in Figure 2, over point A for the vertical line of AB to pay DC extension line at point E, over point E for l_1 vertical line and l_1, l_2 Respectively, at points H, F, then HF⊥l_2. Since AB⊥BC, BC⊥CD, and AE⊥AB are also known, the quadrilateral ABCE is a rectangle, AE = BC, AB = EC, so DE = DC + CE = DC + AB = 50. And AB and l_1 into a 30 ° angle, so ∠ EDF = 30 °, ∠ EAH = 60 °.