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已知三角形的两边和其中一边的对角解三角形是初中代数第四册中解斜三角形这一部分中的难点,教材中是用正弦定理来解决这一类问题的。教参中对已知a、b、A解三角形讨论解的情这个表格虽然很清楚,但学生很难长期记忆。教学实践表明用余弦定理来解决这个问题效果较好。这是因为用余弦定理解这类问题就把三角形解的讨论问题转化为一元二次方程解的讨论问题,学生对此已相当熟悉了。从下面例子可见,这种解法并不烦琐。
The triangles on the opposite sides of the triangle and the triangles on the opposite sides of the triangle are the difficulties in solving the oblique triangle in the fourth volume of junior high school algebra. The textbook uses sine theorem to solve this kind of problem. Although it is clear that the form of discussing the solution of known triangles for a, b, and A is very clear, it is difficult for students to remember for a long time. Teaching practice shows that using the cosine theorem to solve this problem works well. This is because the use of cosine to understand this type of problem transforms the discussion of the triangular solution into the discussion of the solution of the one-dimensional quadratic equation. Students are already quite familiar with it. As can be seen from the following example, this solution is not cumbersome.