1
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讓我們繼續看這個30 60 90三角形

2
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讓我們先回顧一下我們所學的

3
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希望你們還記得

4
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如果我們有一個30 60 90三角形

5
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注意下面的結論只適用於30 60 90三角形

6
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假設斜邊長是h

7
00:00:27,130 --> 00:00:30,990
我們知道30度角的對邊

8
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是三角形最短的邊它的邊長是h除以2

9
00:00:35,570 --> 00:00:36,940
也就是斜邊的一半

10
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我們也知道較長的一邊

11
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也就是60度角的對邊

12
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邊長是根號3除以2乘以h

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現在讓我們用這個結論來解一道題

14
00:00:49,240 --> 00:00:56,650
假設我有這樣一個三角形

15
00:00:56,650 --> 00:00:57,830
它是直角三角形

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這個角是30度

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那麽很容易看出 如果這是30度

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這是90度 這就是60度

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假設斜邊長是12

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並且我們知道這是斜邊

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因爲它與直角相對

22
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這條邊是什麽呢

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這是60度角所對的邊

24
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還是30度角所對的邊

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是30度角朝向它

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是吧

27
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我有意把這個三角形畫得不一樣

28
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30度角朝向這一邊

29
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而且這也是最短的邊

30
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我們知道30度角的對邊

31
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邊長是斜邊的一半

32
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所以如果斜邊是12這條邊就是6

33
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那麽這條邊 60度角所對的邊

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邊長等於根號3除以2乘以斜邊長

35
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所以它就是根號3除以2乘以12

36
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也就等於6乘以根號3

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另一個有趣的現象是

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較長的非斜邊的邊長等於

39
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短邊的邊長的根號3倍

40
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希望你們沒有被我繞糊塗

41
00:02:07,710 --> 00:02:08,980
讓我們再做一道題

42
00:02:09,030 --> 00:02:19,510
假設這是30度 這是直角三角形

43
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而且我告訴你這條邊是5

44
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那麽這條邊長是多少呢

45
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首先 讓我們看看有哪些已知條件

46
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5是哪一條邊

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如果這是30度角

48
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那麽我們知道這就是60度角

49
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所以5是60度角的對邊

50
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x是斜邊

51
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因爲x是90度角的對邊

52
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所以它也是直角三角形的最長邊

53
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按照公式

54
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5等於根號3除以2乘以斜邊

55
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斜邊就是x現在我們只需要解得x

56
00:03:04,480 --> 00:03:08,000
等式兩邊都乘以這個係數的倒數

57
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如果乘以2 根號3

58
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忽略這個

59
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我們得到10除以根號3

60
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而且 這個2和這個2相消

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這個根號3和這的根號3相消最後等於x

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現在看最後一行演算

63
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這已經是正確的答案

64
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但是分母中有根號3

65
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人們通常不喜歡

66
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分母中有無理數

67
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或許我們可以辯論一下爲什麽這樣不好

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但是現在還是讓我們將分母有理化吧

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我們得到了x等於10除以根號3

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爲了將分母有理化

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我們可以將分子分母同

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乘以根號3

73
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因爲只要我們將分子分母

74
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同乘以相同的數 就相當於乘以1

75
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所以這就等於

76
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10乘以根號3 除以根號3乘以根號3

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也就是3

78
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所以x等於10乘以根號3 除以3就是斜邊長

79
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我知道這讓你們有些困惑

80
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如果這是10倍根號3除以3

81
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也就是斜邊長

82
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我們知道30度的對邊

83
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這是30度角 我們知道它的對邊是斜邊的一半

84
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所以它是5倍根號3除以3

85
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總而言之我想這些已經讓你們初步了解了

86
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30 60 90三角形

87
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我認爲現在你們或許可以嘗試

88
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勾股定理更高難度的題目

89
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玩得開心