0:00:00.600,0:00:02.530 在上一个视频中,我们讲了 0:00:02.530,0:00:05.080 一个 30-60-90 的三角形的边长比 0:00:05.080,0:00:06.675 是--如果我们假设最长的边是 x , 0:00:06.675,0:00:08.350 如果斜边是 x , 0:00:08.350,0:00:11.480 那么最短的边长就是 x/2,而这两个边之间的边, 0:00:11.480,0:00:13.690 也就是60°角的对边, 0:00:13.690,0:00:14.890 边长是 3x/2 的平方根。 0:00:14.890,0:00:19.125 或者用另一种方法考虑,如果最短的边是 1, 0:00:19.125,0:00:21.540 我先考虑最短的边,然后是长度居中的边, 0:00:21.540,0:00:22.390 然后是最长的边。 0:00:22.390,0:00:24.500 如果30°角对面的边长是 1, 0:00:24.500,0:00:27.400 那么60°角对面的边长 0:00:27.400,0:00:29.340 就是 它的3倍的平方根。 0:00:29.340,0:00:31.110 它就是 3 的平方根。 0:00:31.110,0:00:33.850 然后,斜边是它的2倍。 0:00:33.850,0:00:35.480 上一个视频中,我们从 x 开始, 0:00:35.480,0:00:37.460 我们说 30°对面的边是 x/2。 0:00:37.460,0:00:40.110 但是,如果 30° 对面的边是 1, 0:00:40.110,0:00:41.270 那么这条边就是它的 2倍。 0:00:41.270,0:00:42.440 它就是 2。 0:00:42.440,0:00:46.120 这里就是30°对面的边, 0:00:46.120,0:00:49.440 60°对面的边,和斜边,也就是 0:00:49.440,0:00:51.030 90°对面的边。 0:00:51.030,0:00:53.800 一般来说,如果你看到 0:00:53.800,0:00:56.570 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。 0:00:56.570,0:00:58.075 0:00:58.075,0:01:02.290 0:01:02.290,0:01:05.099 0:01:05.099,0:01:06.660 0:01:06.660,0:01:08.930 0:01:08.930,0:01:14.510 0:01:14.510,0:01:15.480 0:01:15.480,0:01:17.790 0:01:17.790,0:01:19.440 0:01:19.440,0:01:22.340 0:01:22.340,0:01:25.440 0:01:25.440,0:01:27.380 0:01:27.380,0:01:29.570 0:01:29.570,0:01:32.980 0:01:32.980,0:01:36.649 0:01:36.649,0:01:38.190 0:01:38.190,0:01:40.155 0:01:44.250,0:01:47.140 0:01:47.140,0:01:49.770 0:01:49.770,0:01:51.030 0:01:51.030,0:01:52.870 0:01:52.870,0:01:55.260 0:01:55.260,0:01:56.790 0:01:56.790,0:02:03.470 0:02:03.470,0:02:05.830 0:02:05.830,0:02:06.500 0:02:06.500,0:02:09.851 0:02:09.851,0:02:11.350 0:02:11.350,0:02:14.990 0:02:14.990,0:02:17.440 0:02:17.440,0:02:25.440 0:02:25.440,0:02:27.610 0:02:27.610,0:02:32.060 0:02:32.060,0:02:33.780 0:02:33.780,0:02:38.750 0:02:38.750,0:02:41.850 0:02:41.850,0:02:44.010 0:02:44.010,0:02:50.140 0:02:54.239,0:02:56.030 0:02:56.030,0:02:59.180 0:02:59.180,0:03:01.270 0:03:01.270,0:03:03.180 0:03:03.180,0:03:08.950 0:03:08.950,0:03:10.819 0:03:10.819,0:03:12.610 0:03:12.610,0:03:14.770 0:03:14.770,0:03:18.090 0:03:18.090,0:03:22.740 0:03:22.740,0:03:26.429 0:03:26.429,0:03:27.970 0:03:27.970,0:03:29.740 0:03:29.740,0:03:32.310 0:03:32.310,0:03:37.490 0:03:37.490,0:03:41.566 0:03:41.566,0:03:45.930 0:03:45.930,0:03:48.230 0:03:51.290,0:03:53.420 0:03:53.420,0:03:54.860 0:03:54.860,0:03:57.790 0:03:57.790,0:04:01.290 0:04:01.290,0:04:04.690 0:04:04.690,0:04:07.790 0:04:07.790,0:04:09.790 0:04:09.790,0:04:11.200 0:04:11.200,0:04:13.980 0:04:13.980,0:04:18.230 0:04:18.230,0:04:22.130 0:04:22.130,0:04:23.940 0:04:23.940,0:04:26.650 0:04:26.650,0:04:27.750 0:04:27.750,0:04:30.690 0:04:30.690,0:04:33.640 0:04:33.640,0:04:35.900 0:04:35.900,0:04:37.510 0:04:37.510,0:04:39.790 0:04:39.790,0:04:41.909 0:04:41.909,0:04:43.450 0:04:43.450,0:04:45.970 0:04:45.970,0:04:47.210 0:04:47.210,0:04:49.050 0:04:49.050,0:04:50.370 0:04:50.370,0:04:53.109 0:04:53.109,0:04:55.150 0:04:55.150,0:04:57.920 0:04:57.920,0:05:01.400 0:05:01.400,0:05:03.790 0:05:03.790,0:05:09.190 0:05:09.190,0:05:12.342 0:05:12.342,0:05:14.550 0:05:14.550,0:05:16.820 0:05:16.820,0:05:19.100 0:05:19.100,0:05:21.690 0:05:21.690,0:05:22.690 0:05:28.740,0:05:30.010 0:05:30.010,0:05:33.680 0:05:33.680,0:05:38.800 0:05:38.800,0:05:41.820