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