[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.00,0:00:00.86,Default,,0000,0000,0000,,
Dialogue: 0,0:00:00.86,0:00:03.25,Default,,0000,0000,0000,,Let's continue with the\N30, 60, 90 triangles.
Dialogue: 0,0:00:03.25,0:00:06.48,Default,,0000,0000,0000,,
Dialogue: 0,0:00:06.48,0:00:09.64,Default,,0000,0000,0000,,So just review what we just\Nlearned, or hopefully learned--
Dialogue: 0,0:00:09.64,0:00:15.91,Default,,0000,0000,0000,,at minimum what we just saw,\N--is if we have a 30, 60, 90 --
Dialogue: 0,0:00:15.91,0:00:18.38,Default,,0000,0000,0000,,and once again, remember: this\Nis only applies to 30, 60, 90
Dialogue: 0,0:00:18.38,0:00:26.56,Default,,0000,0000,0000,,triangles --and if I were to\Nsay the hypotenuse is of length
Dialogue: 0,0:00:26.56,0:00:31.32,Default,,0000,0000,0000,,h, we learned that the side\Nopposite the 30-degree angle,
Dialogue: 0,0:00:31.32,0:00:34.34,Default,,0000,0000,0000,,and this is the shortest side\Nof the triangle, is going to be
Dialogue: 0,0:00:34.34,0:00:37.27,Default,,0000,0000,0000,,h over 2, or 1/2 times\Nthe hypotenuse.
Dialogue: 0,0:00:37.27,0:00:40.24,Default,,0000,0000,0000,,And we also learned that the\Nlonger side, or the side
Dialogue: 0,0:00:40.24,0:00:42.81,Default,,0000,0000,0000,,opposite the 60-degree side,\Nis equal to the square
Dialogue: 0,0:00:42.81,0:00:46.84,Default,,0000,0000,0000,,root of 3 over 2 times h.
Dialogue: 0,0:00:46.84,0:00:50.64,Default,,0000,0000,0000,,So let's do a problem where\Nwe use this information.
Dialogue: 0,0:00:50.64,0:00:56.37,Default,,0000,0000,0000,,Let's say I had this\Ntriangle right here.
Dialogue: 0,0:00:56.37,0:00:58.01,Default,,0000,0000,0000,,It's a 90-degree triangle;\Nlet's say that this
Dialogue: 0,0:00:58.01,0:01:00.69,Default,,0000,0000,0000,,is 30 degrees.
Dialogue: 0,0:01:00.69,0:01:02.75,Default,,0000,0000,0000,,And we could also figure out\Nobviously if that's 30, this
Dialogue: 0,0:01:02.75,0:01:07.04,Default,,0000,0000,0000,,is 90, that this is\Nalso 60 degrees.
Dialogue: 0,0:01:07.04,0:01:10.51,Default,,0000,0000,0000,,And let's say that the\Nhypotenuse is 12.
Dialogue: 0,0:01:10.51,0:01:12.30,Default,,0000,0000,0000,,The length is 12 and we know\Nthat this is the hypotenuse
Dialogue: 0,0:01:12.30,0:01:14.98,Default,,0000,0000,0000,,because it's opposite\Nthe right angle.
Dialogue: 0,0:01:14.98,0:01:18.63,Default,,0000,0000,0000,,What is the side right here?
Dialogue: 0,0:01:18.63,0:01:21.84,Default,,0000,0000,0000,,Well, is the side opposite the\N60-degree angle, or is it
Dialogue: 0,0:01:21.84,0:01:23.91,Default,,0000,0000,0000,,opposite the 30-degree angle?
Dialogue: 0,0:01:23.91,0:01:26.46,Default,,0000,0000,0000,,It's the 30-degree angle\Nthat opens into it, right?
Dialogue: 0,0:01:26.46,0:01:28.65,Default,,0000,0000,0000,,I drew this triangle a little\Nbit different on purpose.
Dialogue: 0,0:01:28.65,0:01:32.05,Default,,0000,0000,0000,,The 30-degree angle opens up\Ninto this side, and it's
Dialogue: 0,0:01:32.05,0:01:34.06,Default,,0000,0000,0000,,also the shortest side.
Dialogue: 0,0:01:34.06,0:01:37.36,Default,,0000,0000,0000,,We learned that the side\Nopposite the 30-degree angle is
Dialogue: 0,0:01:37.36,0:01:40.68,Default,,0000,0000,0000,,half the hypotenuse, so the\Nhypotenuse is 12;
Dialogue: 0,0:01:40.68,0:01:42.86,Default,,0000,0000,0000,,this would be 6.
Dialogue: 0,0:01:42.86,0:01:46.31,Default,,0000,0000,0000,,And this side, which is\Nopposite the 60-degree side, is
Dialogue: 0,0:01:46.31,0:01:49.73,Default,,0000,0000,0000,,equal to the square root of 3\Nover 2 times the hypotenuse.
Dialogue: 0,0:01:49.73,0:01:54.69,Default,,0000,0000,0000,,So it's the square root of 3\Nover 2 times 12, or it's just
Dialogue: 0,0:01:54.69,0:01:58.15,Default,,0000,0000,0000,,equal to 6 square roots of 3.
Dialogue: 0,0:01:58.15,0:02:01.15,Default,,0000,0000,0000,,Another interesting thing is,\Nof course, the longer
Dialogue: 0,0:02:01.15,0:02:04.60,Default,,0000,0000,0000,,non-hypotenuse side is square\Nroot of 3 times longer
Dialogue: 0,0:02:04.60,0:02:06.27,Default,,0000,0000,0000,,than the short side.
Dialogue: 0,0:02:06.27,0:02:07.81,Default,,0000,0000,0000,,I don't confuse you too much.
Dialogue: 0,0:02:07.81,0:02:08.66,Default,,0000,0000,0000,,Let's do another one.
Dialogue: 0,0:02:08.66,0:02:15.01,Default,,0000,0000,0000,,
Dialogue: 0,0:02:15.01,0:02:20.80,Default,,0000,0000,0000,,Let's say this is 30 degrees--\Nit's our right triangle --and I
Dialogue: 0,0:02:20.80,0:02:28.39,Default,,0000,0000,0000,,were to tell you that this side\Nright here is 5, what is
Dialogue: 0,0:02:28.39,0:02:29.90,Default,,0000,0000,0000,,the length of this side?
Dialogue: 0,0:02:29.90,0:02:33.97,Default,,0000,0000,0000,,
Dialogue: 0,0:02:33.97,0:02:35.75,Default,,0000,0000,0000,,Well first of all let's\Nfigure out what we have.
Dialogue: 0,0:02:35.75,0:02:37.39,Default,,0000,0000,0000,,5 is which side?
Dialogue: 0,0:02:37.39,0:02:39.54,Default,,0000,0000,0000,,So if this is 30 degrees,\Nwe know that this is
Dialogue: 0,0:02:39.54,0:02:41.99,Default,,0000,0000,0000,,going to be 60 degrees.
Dialogue: 0,0:02:41.99,0:02:47.01,Default,,0000,0000,0000,,So 5 is opposite the 60-degree\Nside, and x is the hypotenuse.
Dialogue: 0,0:02:47.01,0:02:49.84,Default,,0000,0000,0000,,Since x is opposite the\N90-degree side, it's also
Dialogue: 0,0:02:49.84,0:02:53.01,Default,,0000,0000,0000,,the longest side of\Nthe right triangle.
Dialogue: 0,0:02:53.01,0:02:57.91,Default,,0000,0000,0000,,So we know from our formula\Nthat 5 is equal to the square
Dialogue: 0,0:02:57.91,0:03:00.94,Default,,0000,0000,0000,,root of 3 over 2 times the\Nhypotenuse, which in
Dialogue: 0,0:03:00.94,0:03:02.85,Default,,0000,0000,0000,,this example is x.
Dialogue: 0,0:03:02.85,0:03:04.24,Default,,0000,0000,0000,,And now we just solve for x.
Dialogue: 0,0:03:04.24,0:03:06.77,Default,,0000,0000,0000,,We can multiply both\Nsides by the inverse
Dialogue: 0,0:03:06.77,0:03:07.86,Default,,0000,0000,0000,,of this coefficient.
Dialogue: 0,0:03:07.86,0:03:19.71,Default,,0000,0000,0000,,So if you just multiply 2 times\Nthe square root of 3-- can
Dialogue: 0,0:03:19.71,0:03:25.03,Default,,0000,0000,0000,,ignore this --we get 10 over\Nthe square root of three here.
Dialogue: 0,0:03:25.03,0:03:27.14,Default,,0000,0000,0000,,And, of course, this 2\Ncancels out with this 2.
Dialogue: 0,0:03:27.14,0:03:28.67,Default,,0000,0000,0000,,This square root of 3 cancels\Nout this square root
Dialogue: 0,0:03:28.67,0:03:30.97,Default,,0000,0000,0000,,of 3 is equal to x.
Dialogue: 0,0:03:30.97,0:03:33.51,Default,,0000,0000,0000,,And now if you watched the last\Ncouple of presentations, you
Dialogue: 0,0:03:33.51,0:03:36.69,Default,,0000,0000,0000,,realize that this could be the\Nright answer, but we have a
Dialogue: 0,0:03:36.69,0:03:39.66,Default,,0000,0000,0000,,square root of 3 in the\Ndenominator, which people don't
Dialogue: 0,0:03:39.66,0:03:42.98,Default,,0000,0000,0000,,like because it's an irrational\Nnumber in the denominator.
Dialogue: 0,0:03:42.98,0:03:44.69,Default,,0000,0000,0000,,And I guess we could\Nhave a debate as to
Dialogue: 0,0:03:44.69,0:03:46.01,Default,,0000,0000,0000,,why that might be bad.
Dialogue: 0,0:03:46.01,0:03:49.87,Default,,0000,0000,0000,,So let's rationalize\Nthis denominator.
Dialogue: 0,0:03:49.87,0:03:55.15,Default,,0000,0000,0000,,We say x is equal to 10 over\Nthe square to 3; to rationalize
Dialogue: 0,0:03:55.15,0:03:57.75,Default,,0000,0000,0000,,this denominator we can\Nmultiply the numerator and the
Dialogue: 0,0:03:57.75,0:03:59.91,Default,,0000,0000,0000,,denominator by the\Nsquare root of 3.
Dialogue: 0,0:03:59.91,0:04:02.67,Default,,0000,0000,0000,,Because as long as we multiply\Nthe numerator and the
Dialogue: 0,0:04:02.67,0:04:05.28,Default,,0000,0000,0000,,denominator by the same thing,\Nit's like multiplying by 1.
Dialogue: 0,0:04:05.28,0:04:09.79,Default,,0000,0000,0000,,So this is equal to 10 square\Nroots of 3 over square root of
Dialogue: 0,0:04:09.79,0:04:12.100,Default,,0000,0000,0000,,3 times square of 3;\Nwell that's just 3.
Dialogue: 0,0:04:12.100,0:04:16.21,Default,,0000,0000,0000,,So x equals 10 square\Nroots of 3 over 3.
Dialogue: 0,0:04:16.21,0:04:17.87,Default,,0000,0000,0000,,That's the hypotenuse.
Dialogue: 0,0:04:17.87,0:04:18.99,Default,,0000,0000,0000,,I know I confused you.
Dialogue: 0,0:04:18.99,0:04:22.92,Default,,0000,0000,0000,,And, of course, if this is 10\Nsquare root of 3 over 3--
Dialogue: 0,0:04:22.92,0:04:26.60,Default,,0000,0000,0000,,that's the hypotenuse --we know\Nthat the 30-degree side-- this
Dialogue: 0,0:04:26.60,0:04:28.82,Default,,0000,0000,0000,,is 30 degrees --we know the\N30-degree side is half of
Dialogue: 0,0:04:28.82,0:04:35.43,Default,,0000,0000,0000,,that, so it's 5 square\Nroot of 3 over 3.
Dialogue: 0,0:04:35.43,0:04:38.10,Default,,0000,0000,0000,,Anyway, I think that might\Ngive you a sense of the
Dialogue: 0,0:04:38.10,0:04:40.23,Default,,0000,0000,0000,,30, 60, 90 triangles.
Dialogue: 0,0:04:40.23,0:04:43.98,Default,,0000,0000,0000,,I think you might be ready now\Nto try some of the level two
Dialogue: 0,0:04:43.98,0:04:46.08,Default,,0000,0000,0000,,Pythagorean Theorem problems.
Dialogue: 0,0:04:46.08,0:04:47.60,Default,,0000,0000,0000,,Have fun.
Dialogue: 0,0:04:47.60,0:04:48.39,Default,,0000,0000,0000,,