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让我们继续看这个30 60 90三角形

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让我们先回顾一下我们所学的

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希望你们还记得

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如果我们有一个30 60 90三角形

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注意下面的结论只适用于30 60 90三角形

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假设斜边长是h

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我们知道30度角的对边

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是三角形最短的边它的边长是h除以2

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也就是斜边的一半

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我们也知道较长的一边

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也就是60度角的对边

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边长是根号3除以2乘以h

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现在让我们用这个结论来解一道题

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假设我有这样一个三角形

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它是直角三角形

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这个角是30度

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那么很容易看出 如果这是30度

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这是90度 这就是60度

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假设斜边长是12

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并且我们知道这是斜边

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因为它与直角相对

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这条边是什么呢

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这是60度角所对的边

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还是30度角所对的边

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是30度角朝向它

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是吧

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我有意把这个三角形画得不一样

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30度角朝向这一边

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而且这也是最短的边

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我们知道30度角的对边

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边长是斜边的一半

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所以如果斜边是12这条边就是6

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那么这条边 60度角所对的边

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边长等于根号3除以2乘以斜边长

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所以它就是根号3除以2乘以12

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也就等于6乘以根号3

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另一个有趣的现象是

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较长的非斜边的边长等于

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短边的边长的根号3倍

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希望你们没有被我绕糊涂

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让我们再做一道题

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假设这是30度 这是直角三角形

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而且我告诉你这条边是5

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那么这条边长是多少呢

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首先 让我们看看有哪些已知条件

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5是哪一条边

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如果这是30度角

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那么我们知道这就是60度角

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所以5是60度角的对边

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x是斜边

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因为x是90度角的对边

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所以它也是直角三角形的最长边

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按照公式

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5等于根号3除以2乘以斜边

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斜边就是x现在我们只需要解得x

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等式两边都乘以这个系数的倒数

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如果乘以2 根号3

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忽略这个

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我们得到10除以根号3

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而且 这个2和这个2相消

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这个根号3和这的根号3相消最后等于x

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现在看最后一行演算

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这已经是正确的答案

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但是分母中有根号3

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人们通常不喜欢

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分母中有无理数

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或许我们可以辩论一下为什么这样不好

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但是现在还是让我们将分母有理化吧

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我们得到了x等于10除以根号3

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为了将分母有理化

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我们可以将分子分母同

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乘以根号3

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因为只要我们将分子分母

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同乘以相同的数 就相当于乘以1

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所以这就等于

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10乘以根号3 除以根号3乘以根号3

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也就是3

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所以x等于10乘以根号3 除以3就是斜边长

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我知道这让你们有些困惑

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如果这是10倍根号3除以3

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也就是斜边长

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我们知道30度的对边

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这是30度角 我们知道它的对边是斜边的一半

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所以它是5倍根号3除以3

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总而言之我想这些已经让你们初步了解了

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30 60 90三角形

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我认为现在你们或许可以尝试

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勾股定理更高难度的题目

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玩得开心