1 00:00:00,600 --> 00:00:02,530 在上一个视频中,我们讲了 2 00:00:02,530 --> 00:00:05,080 一个 30-60-90 的三角形的边长比 3 00:00:05,080 --> 00:00:06,675 是--如果我们假设最长的边是 x , 4 00:00:06,675 --> 00:00:08,350 如果斜边是 x , 5 00:00:08,350 --> 00:00:11,480 那么最短的边长就是 x/2,而这两个边之间的边, 6 00:00:11,480 --> 00:00:13,690 也就是60°角的对边, 7 00:00:13,690 --> 00:00:14,890 边长是 3x/2 的平方根。 8 00:00:14,890 --> 00:00:19,125 或者用另一种方法考虑,如果最短的边是 1, 9 00:00:19,125 --> 00:00:21,540 我先考虑最短的边,然后是长度居中的边, 10 00:00:21,540 --> 00:00:22,390 然后是最长的边。 11 00:00:22,390 --> 00:00:24,500 如果30°角对面的边长是 1, 12 00:00:24,500 --> 00:00:27,400 那么60°角对面的边长 13 00:00:27,400 --> 00:00:29,340 就是 它的3倍的平方根。 14 00:00:29,340 --> 00:00:31,110 它就是 3 的平方根。 15 00:00:31,110 --> 00:00:33,850 然后,斜边是它的2倍。 16 00:00:33,850 --> 00:00:35,480 上一个视频中,我们从 x 开始, 17 00:00:35,480 --> 00:00:37,460 我们说 30°对面的边是 x/2。 18 00:00:37,460 --> 00:00:40,110 但是,如果 30° 对面的边是 1, 19 00:00:40,110 --> 00:00:41,270 那么这条边就是它的 2倍。 20 00:00:41,270 --> 00:00:42,440 它就是 2。 21 00:00:42,440 --> 00:00:46,120 这里就是30°对面的边, 22 00:00:46,120 --> 00:00:49,440 60°对面的边,和斜边,也就是 23 00:00:49,440 --> 00:00:51,030 90°对面的边。 24 00:00:51,030 --> 00:00:53,800 一般来说,如果你看到 25 00:00:53,800 --> 00:00:56,570 任何三角形有这样的边长比,你就可以说,那是一个 30-60-90 的三角形。 26 00:00:56,570 --> 00:00:58,075 27 00:00:58,075 --> 00:01:02,290 28 00:01:02,290 --> 00:01:05,099 29 00:01:05,099 --> 00:01:06,660 30 00:01:06,660 --> 00:01:08,930 31 00:01:08,930 --> 00:01:14,510 32 00:01:14,510 --> 00:01:15,480 33 00:01:15,480 --> 00:01:17,790 34 00:01:17,790 --> 00:01:19,440 35 00:01:19,440 --> 00:01:22,340 36 00:01:22,340 --> 00:01:25,440 37 00:01:25,440 --> 00:01:27,380 38 00:01:27,380 --> 00:01:29,570 39 00:01:29,570 --> 00:01:32,980 40 00:01:32,980 --> 00:01:36,649 41 00:01:36,649 --> 00:01:38,190 42 00:01:38,190 --> 00:01:40,155 43 00:01:44,250 --> 00:01:47,140 44 00:01:47,140 --> 00:01:49,770 45 00:01:49,770 --> 00:01:51,030 46 00:01:51,030 --> 00:01:52,870 47 00:01:52,870 --> 00:01:55,260 48 00:01:55,260 --> 00:01:56,790 49 00:01:56,790 --> 00:02:03,470 50 00:02:03,470 --> 00:02:05,830 51 00:02:05,830 --> 00:02:06,500 52 00:02:06,500 --> 00:02:09,851 53 00:02:09,851 --> 00:02:11,350 54 00:02:11,350 --> 00:02:14,990 55 00:02:14,990 --> 00:02:17,440 56 00:02:17,440 --> 00:02:25,440 57 00:02:25,440 --> 00:02:27,610 58 00:02:27,610 --> 00:02:32,060 59 00:02:32,060 --> 00:02:33,780 60 00:02:33,780 --> 00:02:38,750 61 00:02:38,750 --> 00:02:41,850 62 00:02:41,850 --> 00:02:44,010 63 00:02:44,010 --> 00:02:50,140 64 00:02:54,239 --> 00:02:56,030 65 00:02:56,030 --> 00:02:59,180 66 00:02:59,180 --> 00:03:01,270 67 00:03:01,270 --> 00:03:03,180 68 00:03:03,180 --> 00:03:08,950 69 00:03:08,950 --> 00:03:10,819 70 00:03:10,819 --> 00:03:12,610 71 00:03:12,610 --> 00:03:14,770 72 00:03:14,770 --> 00:03:18,090 73 00:03:18,090 --> 00:03:22,740 74 00:03:22,740 --> 00:03:26,429 75 00:03:26,429 --> 00:03:27,970 76 00:03:27,970 --> 00:03:29,740 77 00:03:29,740 --> 00:03:32,310 78 00:03:32,310 --> 00:03:37,490 79 00:03:37,490 --> 00:03:41,566 80 00:03:41,566 --> 00:03:45,930 81 00:03:45,930 --> 00:03:48,230 82 00:03:51,290 --> 00:03:53,420 83 00:03:53,420 --> 00:03:54,860 84 00:03:54,860 --> 00:03:57,790 85 00:03:57,790 --> 00:04:01,290 86 00:04:01,290 --> 00:04:04,690 87 00:04:04,690 --> 00:04:07,790 88 00:04:07,790 --> 00:04:09,790 89 00:04:09,790 --> 00:04:11,200 90 00:04:11,200 --> 00:04:13,980 91 00:04:13,980 --> 00:04:18,230 92 00:04:18,230 --> 00:04:22,130 93 00:04:22,130 --> 00:04:23,940 94 00:04:23,940 --> 00:04:26,650 95 00:04:26,650 --> 00:04:27,750 96 00:04:27,750 --> 00:04:30,690 97 00:04:30,690 --> 00:04:33,640 98 00:04:33,640 --> 00:04:35,900 99 00:04:35,900 --> 00:04:37,510 100 00:04:37,510 --> 00:04:39,790 101 00:04:39,790 --> 00:04:41,909 102 00:04:41,909 --> 00:04:43,450 103 00:04:43,450 --> 00:04:45,970 104 00:04:45,970 --> 00:04:47,210 105 00:04:47,210 --> 00:04:49,050 106 00:04:49,050 --> 00:04:50,370 107 00:04:50,370 --> 00:04:53,109 108 00:04:53,109 --> 00:04:55,150 109 00:04:55,150 --> 00:04:57,920 110 00:04:57,920 --> 00:05:01,400 111 00:05:01,400 --> 00:05:03,790 112 00:05:03,790 --> 00:05:09,190 113 00:05:09,190 --> 00:05:12,342 114 00:05:12,342 --> 00:05:14,550 115 00:05:14,550 --> 00:05:16,820 116 00:05:16,820 --> 00:05:19,100 117 00:05:19,100 --> 00:05:21,690 118 00:05:21,690 --> 00:05:22,690 119 00:05:28,740 --> 00:05:30,010 120 00:05:30,010 --> 00:05:33,680 121 00:05:33,680 --> 00:05:38,800 122 00:05:38,800 --> 00:05:41,820