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在一些刊物上经常见到用三角方法解几何题的文章,有些解法很简练,值得学习和提倡。为了引导学生开拓思路,一题多解,有些三角题也可用几何方法解。现举几例如下: 例1 已知tgθ=1/2,tgφ=1/3,并且θ,φ都是锐角,求证θ+φ=45°。(六年制重点中学高中代数第一册,p.184,习题十、11题)。证∵θ、φ都是锐角,且tgθ<1,tgφ<1,∴0<θ<45°,0<φ<45°,0<θ+φ<90°。如图1,作线段AB=5,在AB上取AD=2;作CD⊥AB,D为垂足,使
In some publications, it is common to see trigonometric methods for solving geometric problems. Some solutions are concise and worth learning and advocating. In order to guide students to develop ideas, there are many solutions to the problem, and some triangular problems can also be solved by geometric methods. Here are some examples: Example 1 It is known that tg θ = 1/2, tg φ = 1/3, and θ, φ are all acute angles, and it is verified that θ + φ = 45°. (The first volume of the six-year key middle school high school algebra algebra, p.184, exercises 10 and 11). ∵ and φ are all acute angles, and tgθ<1, tgφ<1, ∴0<θ<45°, 0<φ<45°, and 0<θ+φ<90°. As shown in Figure 1, for the line segment AB = 5, take AD = 2 on AB; for CD ⊥ AB, D for the foot, so that