[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:01.50,0:00:03.43,Default,,0000,0000,0000,,Sorry for starting the\Npresentation with a cough.
Dialogue: 0,0:00:03.43,0:00:06.22,Default,,0000,0000,0000,,I think I still have a little\Nbit of a bug going around.
Dialogue: 0,0:00:06.22,0:00:10.98,Default,,0000,0000,0000,,But now I want to continue\Nwith the 45-45-90 triangles.
Dialogue: 0,0:00:10.98,0:00:15.19,Default,,0000,0000,0000,,So in the last presentation we\Nlearned that either side of a
Dialogue: 0,0:00:15.19,0:00:19.83,Default,,0000,0000,0000,,45-45-90 triangle that isn't\Nthe hypotenuse is equal to the
Dialogue: 0,0:00:19.83,0:00:25.60,Default,,0000,0000,0000,,square route of 2 over 2\Ntimes the hypotenuse.
Dialogue: 0,0:00:25.60,0:00:26.85,Default,,0000,0000,0000,,Let's do a couple\Nof more problems.
Dialogue: 0,0:00:26.85,0:00:30.68,Default,,0000,0000,0000,,So if I were to tell you that\Nthe hypotenuse of this
Dialogue: 0,0:00:30.68,0:00:33.01,Default,,0000,0000,0000,,triangle-- once again,\Nthis only works for
Dialogue: 0,0:00:33.01,0:00:35.76,Default,,0000,0000,0000,,45-45-90 triangles.
Dialogue: 0,0:00:35.76,0:00:37.87,Default,,0000,0000,0000,,And if I just draw one 45\Nyou know the other angle's
Dialogue: 0,0:00:37.87,0:00:39.78,Default,,0000,0000,0000,,got to be 45 as well.
Dialogue: 0,0:00:39.78,0:00:42.96,Default,,0000,0000,0000,,If I told you that the\Nhypotenuse here is,
Dialogue: 0,0:00:42.96,0:00:44.69,Default,,0000,0000,0000,,let me say, 10.
Dialogue: 0,0:00:44.69,0:00:46.51,Default,,0000,0000,0000,,We know this is a hypotenuse\Nbecause it's opposite
Dialogue: 0,0:00:46.51,0:00:48.34,Default,,0000,0000,0000,,the right angle.
Dialogue: 0,0:00:48.34,0:00:50.68,Default,,0000,0000,0000,,And then I would ask you\Nwhat this side is, x.
Dialogue: 0,0:00:50.68,0:00:54.30,Default,,0000,0000,0000,,Well we know that x is equal\Nto the square root of 2 over
Dialogue: 0,0:00:54.30,0:00:55.49,Default,,0000,0000,0000,,2 times the hypotenuse.
Dialogue: 0,0:00:55.49,0:01:01.44,Default,,0000,0000,0000,,So that's square root\Nof 2 over 2 times 10.
Dialogue: 0,0:01:01.44,0:01:07.70,Default,,0000,0000,0000,,Or, x is equal to 5\Nsquare roots of 2.
Dialogue: 0,0:01:07.70,0:01:07.99,Default,,0000,0000,0000,,Right?
Dialogue: 0,0:01:07.99,0:01:08.91,Default,,0000,0000,0000,,10 divided by 2.
Dialogue: 0,0:01:08.91,0:01:12.16,Default,,0000,0000,0000,,So x is equal to 5\Nsquare roots of 2.
Dialogue: 0,0:01:12.16,0:01:15.63,Default,,0000,0000,0000,,And we know that this side\Nand this side are equal.
Dialogue: 0,0:01:15.63,0:01:15.90,Default,,0000,0000,0000,,Right?
Dialogue: 0,0:01:15.90,0:01:18.49,Default,,0000,0000,0000,,I guess we know this is an\Nisosceles triangle because
Dialogue: 0,0:01:18.49,0:01:20.28,Default,,0000,0000,0000,,these two angles are the same.
Dialogue: 0,0:01:20.28,0:01:23.77,Default,,0000,0000,0000,,So we also that this\Nside is 5 over 2.
Dialogue: 0,0:01:23.77,0:01:25.83,Default,,0000,0000,0000,,And if you're not\Nsure, try it out.
Dialogue: 0,0:01:25.83,0:01:27.46,Default,,0000,0000,0000,,Let's try the\NPythagorean theorem.
Dialogue: 0,0:01:27.46,0:01:32.05,Default,,0000,0000,0000,,We know from the Pythagorean\Ntheorem that 5 root 2 squared,
Dialogue: 0,0:01:32.05,0:01:37.42,Default,,0000,0000,0000,,plus 5 root 2 squared is equal\Nto the hypotenuse squared,
Dialogue: 0,0:01:37.42,0:01:39.09,Default,,0000,0000,0000,,where the hypotenuse is 10.
Dialogue: 0,0:01:39.09,0:01:41.13,Default,,0000,0000,0000,,Is equal to 100.
Dialogue: 0,0:01:41.13,0:01:43.17,Default,,0000,0000,0000,,Or this is just 25 times 2.
Dialogue: 0,0:01:43.17,0:01:43.86,Default,,0000,0000,0000,,So that's 50.
Dialogue: 0,0:01:48.25,0:01:49.59,Default,,0000,0000,0000,,But this is 100 up here.
Dialogue: 0,0:01:49.59,0:01:51.38,Default,,0000,0000,0000,,Is equal to 100.
Dialogue: 0,0:01:51.38,0:01:53.78,Default,,0000,0000,0000,,And we know, of course,\Nthat this is true.
Dialogue: 0,0:01:53.78,0:01:54.62,Default,,0000,0000,0000,,So it worked.
Dialogue: 0,0:01:54.62,0:01:56.29,Default,,0000,0000,0000,,We proved it using the\NPythagorean theorem, and
Dialogue: 0,0:01:56.29,0:01:57.74,Default,,0000,0000,0000,,that's actually how we\Ncame up with this formula
Dialogue: 0,0:01:57.74,0:01:59.26,Default,,0000,0000,0000,,in the first place.
Dialogue: 0,0:01:59.26,0:02:00.82,Default,,0000,0000,0000,,Maybe you want to go back to\None of those presentations
Dialogue: 0,0:02:00.82,0:02:03.59,Default,,0000,0000,0000,,if you forget how we\Ncame up with this.
Dialogue: 0,0:02:03.59,0:02:05.89,Default,,0000,0000,0000,,I'm actually now going\Nto introduce another
Dialogue: 0,0:02:05.89,0:02:06.62,Default,,0000,0000,0000,,type of triangle.
Dialogue: 0,0:02:06.62,0:02:11.16,Default,,0000,0000,0000,,And I'm going to do it the same\Nway, by just posing a problem
Dialogue: 0,0:02:11.16,0:02:14.49,Default,,0000,0000,0000,,to you and then using the\NPythagorean theorem
Dialogue: 0,0:02:14.49,0:02:16.98,Default,,0000,0000,0000,,to figure it out.
Dialogue: 0,0:02:16.98,0:02:18.78,Default,,0000,0000,0000,,This is another type\Nof triangle called a
Dialogue: 0,0:02:18.78,0:02:20.14,Default,,0000,0000,0000,,30-60-90 triangle.
Dialogue: 0,0:02:25.55,0:02:28.22,Default,,0000,0000,0000,,And if I don't have time\Nfor this I will do
Dialogue: 0,0:02:28.22,0:02:31.12,Default,,0000,0000,0000,,another presentation.
Dialogue: 0,0:02:31.12,0:02:33.96,Default,,0000,0000,0000,,Let's say I have a\Nright triangle.
Dialogue: 0,0:02:38.61,0:02:42.71,Default,,0000,0000,0000,,That's not a pretty one,\Nbut we use what we have.
Dialogue: 0,0:02:42.71,0:02:43.92,Default,,0000,0000,0000,,That's a right angle.
Dialogue: 0,0:02:43.92,0:02:48.26,Default,,0000,0000,0000,,And if I were to tell you that\Nthis is a 30 degree angle.
Dialogue: 0,0:02:48.26,0:02:49.94,Default,,0000,0000,0000,,Well we know that the\Nangles in a triangle
Dialogue: 0,0:02:49.94,0:02:51.73,Default,,0000,0000,0000,,have to add up to 180.
Dialogue: 0,0:02:51.73,0:02:56.57,Default,,0000,0000,0000,,So if this is 30, this is 90,\Nand let's say that this is x.
Dialogue: 0,0:02:56.57,0:03:02.40,Default,,0000,0000,0000,,x plus 30 plus 90 is equal to\N180, because the angles in
Dialogue: 0,0:03:02.40,0:03:04.31,Default,,0000,0000,0000,,a triangle add up to 180.
Dialogue: 0,0:03:04.31,0:03:07.77,Default,,0000,0000,0000,,We know that x is equal to 60.
Dialogue: 0,0:03:07.77,0:03:08.60,Default,,0000,0000,0000,,Right?
Dialogue: 0,0:03:08.60,0:03:10.87,Default,,0000,0000,0000,,So this angle is 60.
Dialogue: 0,0:03:10.87,0:03:14.37,Default,,0000,0000,0000,,And this is why it's called a\N30-60-90 triangle-- because
Dialogue: 0,0:03:14.37,0:03:17.32,Default,,0000,0000,0000,,that's the names of the three\Nangles in the triangle.
Dialogue: 0,0:03:17.32,0:03:24.32,Default,,0000,0000,0000,,And if I were to tell you that\Nthe hypotenuse is-- instead of
Dialogue: 0,0:03:24.32,0:03:27.13,Default,,0000,0000,0000,,calling it c, like we always\Ndo, let's call it h-- and I
Dialogue: 0,0:03:27.13,0:03:30.02,Default,,0000,0000,0000,,want to figure out the other\Nsides, how do we do that?
Dialogue: 0,0:03:30.02,0:03:32.70,Default,,0000,0000,0000,,Well we can do that\Nusing pretty much the
Dialogue: 0,0:03:32.70,0:03:34.21,Default,,0000,0000,0000,,Pythagorean theorem.
Dialogue: 0,0:03:34.21,0:03:36.41,Default,,0000,0000,0000,,And here I'm going to\Ndo a little trick.
Dialogue: 0,0:03:36.41,0:03:42.78,Default,,0000,0000,0000,,Let's draw another copy of this\Ntriangle, but flip it over
Dialogue: 0,0:03:42.78,0:03:45.99,Default,,0000,0000,0000,,draw it the other side.
Dialogue: 0,0:03:45.99,0:03:47.95,Default,,0000,0000,0000,,And this is the same triangle,\Nit's just facing the
Dialogue: 0,0:03:47.95,0:03:48.69,Default,,0000,0000,0000,,other direction.
Dialogue: 0,0:03:48.69,0:03:48.91,Default,,0000,0000,0000,,Right?
Dialogue: 0,0:03:48.91,0:03:51.04,Default,,0000,0000,0000,,If this is 90 degrees\Nwe know that these two
Dialogue: 0,0:03:51.04,0:03:53.14,Default,,0000,0000,0000,,angles are supplementary.
Dialogue: 0,0:03:53.14,0:03:55.89,Default,,0000,0000,0000,,You might want to review the\Nangles module if you forget
Dialogue: 0,0:03:55.89,0:03:58.98,Default,,0000,0000,0000,,that two angles that share kind\Nof this common line would
Dialogue: 0,0:03:58.98,0:04:00.00,Default,,0000,0000,0000,,add up to 180 degrees.
Dialogue: 0,0:04:00.00,0:04:01.68,Default,,0000,0000,0000,,So this is 90, this\Nwill also be 90.
Dialogue: 0,0:04:01.68,0:04:02.39,Default,,0000,0000,0000,,And you can eyeball it.
Dialogue: 0,0:04:02.39,0:04:04.01,Default,,0000,0000,0000,,It makes sense.
Dialogue: 0,0:04:04.01,0:04:06.04,Default,,0000,0000,0000,,And since we flip it, this\Ntriangle is the exact
Dialogue: 0,0:04:06.04,0:04:06.89,Default,,0000,0000,0000,,same triangle as this.
Dialogue: 0,0:04:06.89,0:04:09.13,Default,,0000,0000,0000,,It's just flipped\Nover the other side.
Dialogue: 0,0:04:09.13,0:04:12.40,Default,,0000,0000,0000,,We also know that this\Nangle is 30 degrees.
Dialogue: 0,0:04:12.40,0:04:16.51,Default,,0000,0000,0000,,And we also know that this\Nangle is 60 degrees.
Dialogue: 0,0:04:16.51,0:04:18.19,Default,,0000,0000,0000,,Right?
Dialogue: 0,0:04:18.19,0:04:20.45,Default,,0000,0000,0000,,Well if this angle is 30\Ndegrees and this angle is 30
Dialogue: 0,0:04:20.45,0:04:26.49,Default,,0000,0000,0000,,degrees, we also know that this\Nlarger angle-- goes all the way
Dialogue: 0,0:04:26.49,0:04:30.23,Default,,0000,0000,0000,,from here to here--\Nis 60 degrees.
Dialogue: 0,0:04:30.23,0:04:31.77,Default,,0000,0000,0000,,Right?
Dialogue: 0,0:04:31.77,0:04:34.76,Default,,0000,0000,0000,,Well if this angle is 60\Ndegrees, this top angle is 60
Dialogue: 0,0:04:34.76,0:04:38.92,Default,,0000,0000,0000,,degrees, and this angle on the\Nright is 60 degrees, then we
Dialogue: 0,0:04:38.92,0:04:43.91,Default,,0000,0000,0000,,know from the theorem that we\Nlearned when we did 45-45-90
Dialogue: 0,0:04:43.91,0:04:47.86,Default,,0000,0000,0000,,triangles that if these two\Nangles are the same then the
Dialogue: 0,0:04:47.86,0:04:52.03,Default,,0000,0000,0000,,sides that they don't share\Nhave to be the same as well.
Dialogue: 0,0:04:52.03,0:04:53.44,Default,,0000,0000,0000,,So what are the sides\Nthey don't share?
Dialogue: 0,0:04:53.44,0:04:55.49,Default,,0000,0000,0000,,Well, it's this side\Nand this side.
Dialogue: 0,0:04:55.49,0:04:58.72,Default,,0000,0000,0000,,So if this side is h\Nthen this side is h.
Dialogue: 0,0:04:58.72,0:05:01.20,Default,,0000,0000,0000,,Right?
Dialogue: 0,0:05:01.20,0:05:03.68,Default,,0000,0000,0000,,But this angle is\Nalso 60 degrees.
Dialogue: 0,0:05:03.68,0:05:07.60,Default,,0000,0000,0000,,So if we look at this 60\Ndegrees and this 60 degrees, we
Dialogue: 0,0:05:07.60,0:05:10.76,Default,,0000,0000,0000,,know that the sides that they\Ndon't share are also equal.
Dialogue: 0,0:05:10.76,0:05:13.80,Default,,0000,0000,0000,,Well they share this side, so\Nthe sides that they don't share
Dialogue: 0,0:05:13.80,0:05:15.37,Default,,0000,0000,0000,,are this side and this side.
Dialogue: 0,0:05:15.37,0:05:19.46,Default,,0000,0000,0000,,So this side is h, we also\Nknow that this side is h.
Dialogue: 0,0:05:19.46,0:05:21.27,Default,,0000,0000,0000,,Right?
Dialogue: 0,0:05:21.27,0:05:23.47,Default,,0000,0000,0000,,So it turns out that if you\Nhave 60 degrees, 60 degrees,
Dialogue: 0,0:05:23.47,0:05:26.68,Default,,0000,0000,0000,,and 60 degrees that all the\Nsides have the same lengths, or
Dialogue: 0,0:05:26.68,0:05:27.81,Default,,0000,0000,0000,,it's an equilateral triangle.
Dialogue: 0,0:05:27.81,0:05:29.67,Default,,0000,0000,0000,,And that's something\Nto keep in mind.
Dialogue: 0,0:05:29.67,0:05:32.08,Default,,0000,0000,0000,,And that makes sense too,\Nbecause an equilateral triangle
Dialogue: 0,0:05:32.08,0:05:33.83,Default,,0000,0000,0000,,is symmetric no matter\Nhow you look at it.
Dialogue: 0,0:05:33.83,0:05:36.03,Default,,0000,0000,0000,,So it makes sense that all of\Nthe angles would be the same
Dialogue: 0,0:05:36.03,0:05:39.37,Default,,0000,0000,0000,,and all of the sides would\Nhave the same length.
Dialogue: 0,0:05:39.37,0:05:40.42,Default,,0000,0000,0000,,But, hm.
Dialogue: 0,0:05:40.42,0:05:43.09,Default,,0000,0000,0000,,When we originally did this\Nproblem we only used half of
Dialogue: 0,0:05:43.09,0:05:44.05,Default,,0000,0000,0000,,this equilateral triangle.
Dialogue: 0,0:05:44.05,0:05:48.97,Default,,0000,0000,0000,,So we know this whole side\Nright here is of length h.
Dialogue: 0,0:05:48.97,0:05:53.67,Default,,0000,0000,0000,,But if that whole side is of\Nlength h, well then this side
Dialogue: 0,0:05:53.67,0:05:56.53,Default,,0000,0000,0000,,right here, just the base of\Nour original triangle-- and I'm
Dialogue: 0,0:05:56.53,0:05:58.48,Default,,0000,0000,0000,,trying to be messy on purpose.
Dialogue: 0,0:05:58.48,0:06:00.49,Default,,0000,0000,0000,,We tried another color.
Dialogue: 0,0:06:00.49,0:06:02.18,Default,,0000,0000,0000,,This is going to be\Nhalf of that side.
Dialogue: 0,0:06:02.18,0:06:03.46,Default,,0000,0000,0000,,Right?
Dialogue: 0,0:06:03.46,0:06:07.89,Default,,0000,0000,0000,,Because that's h over 2,\Nand this is also h over 2.
Dialogue: 0,0:06:07.89,0:06:08.77,Default,,0000,0000,0000,,Right over here.
Dialogue: 0,0:06:12.38,0:06:14.99,Default,,0000,0000,0000,,So if we go back to our\Noriginal triangle, and we said
Dialogue: 0,0:06:14.99,0:06:17.73,Default,,0000,0000,0000,,that this is 30 degrees and\Nthat this is the hypotenuse,
Dialogue: 0,0:06:17.73,0:06:21.54,Default,,0000,0000,0000,,because it's opposite the right\Nangle, we know that the side
Dialogue: 0,0:06:21.54,0:06:26.35,Default,,0000,0000,0000,,opposite the 30 degree side\Nis 1/2 of the hypotenuse.
Dialogue: 0,0:06:26.35,0:06:28.14,Default,,0000,0000,0000,,And just a reminder,\Nhow did we do that?
Dialogue: 0,0:06:28.14,0:06:29.84,Default,,0000,0000,0000,,Well we doubled the triangle.
Dialogue: 0,0:06:29.84,0:06:31.57,Default,,0000,0000,0000,,Turned it into an\Nequilateral triangle.
Dialogue: 0,0:06:31.57,0:06:33.49,Default,,0000,0000,0000,,Figured out this whole\Nside has to be the same
Dialogue: 0,0:06:33.49,0:06:34.49,Default,,0000,0000,0000,,as the hypotenuse.
Dialogue: 0,0:06:34.49,0:06:36.76,Default,,0000,0000,0000,,And this is 1/2 of\Nthat whole side.
Dialogue: 0,0:06:36.76,0:06:38.42,Default,,0000,0000,0000,,So it's 1/2 of the hypotenuse.
Dialogue: 0,0:06:38.42,0:06:39.09,Default,,0000,0000,0000,,So let's remember that.
Dialogue: 0,0:06:39.09,0:06:43.06,Default,,0000,0000,0000,,The side opposite the 30 degree\Nside is 1/2 of the hypotenuse.
Dialogue: 0,0:06:43.06,0:06:46.53,Default,,0000,0000,0000,,Let me redraw that on another\Npage, because I think
Dialogue: 0,0:06:46.53,0:06:48.12,Default,,0000,0000,0000,,this is getting messy.
Dialogue: 0,0:06:48.12,0:06:49.88,Default,,0000,0000,0000,,So going back to what\NI had originally.
Dialogue: 0,0:06:54.63,0:06:56.57,Default,,0000,0000,0000,,This is a right angle.
Dialogue: 0,0:06:56.57,0:06:59.70,Default,,0000,0000,0000,,This is the hypotenuse--\Nthis side right here.
Dialogue: 0,0:06:59.70,0:07:05.08,Default,,0000,0000,0000,,If this is 30 degrees, we just\Nderived that the side opposite
Dialogue: 0,0:07:05.08,0:07:09.83,Default,,0000,0000,0000,,the 30 degrees-- it's like what\Nthe angle is opening into--
Dialogue: 0,0:07:09.83,0:07:12.18,Default,,0000,0000,0000,,that this is equal to\N1/2 the hypotenuse.
Dialogue: 0,0:07:15.19,0:07:17.30,Default,,0000,0000,0000,,If this is equal to 1/2\Nthe hypotenuse then what
Dialogue: 0,0:07:17.30,0:07:19.45,Default,,0000,0000,0000,,is this side equal to?
Dialogue: 0,0:07:19.45,0:07:22.66,Default,,0000,0000,0000,,Well, here we can use the\NPythagorean theorem again.
Dialogue: 0,0:07:22.66,0:07:25.68,Default,,0000,0000,0000,,We know that this side squared\Nplus this side squared-- let's
Dialogue: 0,0:07:25.68,0:07:31.47,Default,,0000,0000,0000,,call this side A-- is\Nequal to h squared.
Dialogue: 0,0:07:31.47,0:07:43.33,Default,,0000,0000,0000,,So we have 1/2 h squared plus A\Nsquared is equal to h squared.
Dialogue: 0,0:07:43.33,0:07:48.37,Default,,0000,0000,0000,,This is equal to h squared\Nover 4 plus A squared,
Dialogue: 0,0:07:48.37,0:07:51.69,Default,,0000,0000,0000,,is equal to h squared.
Dialogue: 0,0:07:51.69,0:07:53.63,Default,,0000,0000,0000,,Well, we subtract h\Nsquared from both sides.
Dialogue: 0,0:07:53.63,0:08:01.27,Default,,0000,0000,0000,,We get A squared is equal to h\Nsquared minus h squared over 4.
Dialogue: 0,0:08:01.27,0:08:07.93,Default,,0000,0000,0000,,So this equals h squared\Ntimes 1 minus 1/4.
Dialogue: 0,0:08:07.93,0:08:14.15,Default,,0000,0000,0000,,This is equal to 3/4 h squared.
Dialogue: 0,0:08:14.15,0:08:17.11,Default,,0000,0000,0000,,And once going that's\Nequal to A squared.
Dialogue: 0,0:08:17.11,0:08:19.71,Default,,0000,0000,0000,,I'm running out of space,\Nso I'm going to go all
Dialogue: 0,0:08:19.71,0:08:21.73,Default,,0000,0000,0000,,the way over here.
Dialogue: 0,0:08:21.73,0:08:27.17,Default,,0000,0000,0000,,So take the square root of both\Nsides, and we get A is equal
Dialogue: 0,0:08:27.17,0:08:30.92,Default,,0000,0000,0000,,to-- the square root of 3/4\Nis the same thing as the
Dialogue: 0,0:08:30.92,0:08:36.27,Default,,0000,0000,0000,,square root of 3 over 2.
Dialogue: 0,0:08:36.27,0:08:40.51,Default,,0000,0000,0000,,And then the square root\Nof h squared is just h.
Dialogue: 0,0:08:41.43,0:08:42.35,Default,,0000,0000,0000,,And this A-- remember,\Nthis isn't an area.
Dialogue: 0,0:08:42.35,0:08:43.99,Default,,0000,0000,0000,,This is what decides the\Nlength of the side.
Dialogue: 0,0:08:43.99,0:08:45.63,Default,,0000,0000,0000,,I probably shouldn't\Nhave used A.
Dialogue: 0,0:08:45.63,0:08:53.07,Default,,0000,0000,0000,,But this is equal to the square\Nroot of 3 over 2, times h.
Dialogue: 0,0:08:53.07,0:08:53.67,Default,,0000,0000,0000,,So there.
Dialogue: 0,0:08:53.67,0:08:56.32,Default,,0000,0000,0000,,We've derived what all the\Nsides relative to the
Dialogue: 0,0:08:56.32,0:08:59.32,Default,,0000,0000,0000,,hypotenuse are of a\N30-60-90 triangle.
Dialogue: 0,0:08:59.32,0:09:01.36,Default,,0000,0000,0000,,So if this is a 60 degree side.
Dialogue: 0,0:09:01.36,0:09:04.75,Default,,0000,0000,0000,,So if we know the hypotenuse\Nand we know this is a 30-60-90
Dialogue: 0,0:09:04.75,0:09:08.08,Default,,0000,0000,0000,,triangle, we know the side\Nopposite the 30 degree side
Dialogue: 0,0:09:08.08,0:09:10.50,Default,,0000,0000,0000,,is 1/2 the hypotenuse.
Dialogue: 0,0:09:10.50,0:09:14.01,Default,,0000,0000,0000,,And we know the side opposite\Nthe 60 degree side is the
Dialogue: 0,0:09:14.01,0:09:18.41,Default,,0000,0000,0000,,square root of 3 over 2,\Ntimes the hypotenuse.
Dialogue: 0,0:09:18.41,0:09:22.25,Default,,0000,0000,0000,,In the next module I'll show\Nyou how using this information,
Dialogue: 0,0:09:22.25,0:09:24.12,Default,,0000,0000,0000,,which you may or may not want\Nto memorize-- it's probably
Dialogue: 0,0:09:24.12,0:09:26.95,Default,,0000,0000,0000,,good to memorize and practice\Nwith, because it'll make you
Dialogue: 0,0:09:26.95,0:09:30.85,Default,,0000,0000,0000,,very fast on standardized\Ntests-- how we can use this
Dialogue: 0,0:09:30.85,0:09:34.74,Default,,0000,0000,0000,,information to solve the sides\Nof a 30-60-90 triangle
Dialogue: 0,0:09:34.74,0:09:35.90,Default,,0000,0000,0000,,very quickly.
Dialogue: 0,0:09:35.90,0:09:37.78,Default,,0000,0000,0000,,See you in the next\Npresentation.