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下面是两道流行的习题解答 :例 1 一平行四边形的两邻边长分别为 2和 4 ,两对角线的夹角为 6 0° ,试求其面积 .解 设平行四边形的对角线的长分别为 2ｘ、2 ｙ ,面积为Ｓ ,则有 Ｓ =4 · 12 ｘｙｓｉｎ6 0° =3ｘｙ .又据余弦定理得 ｘ2 + ｙ2 - 2ｘｙｃｏｓ6 0°=2 2
Here are two popular exercises to answer: Example 1 The length of two adjacent sides of a parallelogram is 2 and 4 respectively, and the angle between two diagonals is 6 0°. Try to find the area. Set the diagonal of the parallelogram. The lengths of the two are 2x, 2y respectively, and the area is S. Then there is S = 4 · 12 xysin6 0° = 3xy. According to the cosine theorem, x2 + y2 - 2xycos6 0° = 2 2