[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:02.36,0:00:04.84,Default,,0000,0000,0000,,INSTRUCTOR: Hello again, Grade Elevens.
Dialogue: 0,0:00:04.84,0:00:08.08,Default,,0000,0000,0000,,I'm just going to run you through one more example of solving a triangle.
Dialogue: 0,0:00:08.08,0:00:12.08,Default,,0000,0000,0000,,The difference with this one is that we are given the lengths of two sides,
Dialogue: 0,0:00:12.08,0:00:14.10,Default,,0000,0000,0000,,and in this case, we have no angles.
Dialogue: 0,0:00:14.10,0:00:16.40,Default,,0000,0000,0000,,I would probably say that most of you,
Dialogue: 0,0:00:16.40,0:00:20.66,Default,,0000,0000,0000,,the first thing that you're going to want to do is to find side y here,
Dialogue: 0,0:00:20.66,0:00:24.44,Default,,0000,0000,0000,,and the way that you're going to do that probably is to use the Pythagorean theorem.
Dialogue: 0,0:00:24.44,0:00:26.36,Default,,0000,0000,0000,,That's great. It would certainly work.
Dialogue: 0,0:00:26.36,0:00:28.88,Default,,0000,0000,0000,,I'm not going to use the Pythagorean theorem because for me,
Dialogue: 0,0:00:28.88,0:00:31.02,Default,,0000,0000,0000,,I think that trig works a little bit better.
Dialogue: 0,0:00:31.02,0:00:32.78,Default,,0000,0000,0000,,Well, it doesn't work better, it works the same,
Dialogue: 0,0:00:32.78,0:00:34.91,Default,,0000,0000,0000,,but I do think it's a little bit quicker.
Dialogue: 0,0:00:34.91,0:00:38.17,Default,,0000,0000,0000,,First, I have to find the angles.
Dialogue: 0,0:00:38.17,0:00:41.02,Default,,0000,0000,0000,,I have no choice. I have to use trig at least once.
Dialogue: 0,0:00:41.02,0:00:43.33,Default,,0000,0000,0000,,I'm going to find angle W first.
Dialogue: 0,0:00:43.33,0:00:49.35,Default,,0000,0000,0000,,What I have to do to do this is recognize that W becomes my reference angle,
Dialogue: 0,0:00:49.35,0:00:52.49,Default,,0000,0000,0000,,and now I have to take a look at what information I have.
Dialogue: 0,0:00:52.49,0:00:56.83,Default,,0000,0000,0000,,I'm looking for the angle, which means I need to have two sides.
Dialogue: 0,0:00:57.19,0:01:02.34,Default,,0000,0000,0000,,I come across from W and I recognize that I have the opposite side.
Dialogue: 0,0:01:02.34,0:01:04.67,Default,,0000,0000,0000,,I obviously don't have the hypotenuse yet,
Dialogue: 0,0:01:04.67,0:01:08.27,Default,,0000,0000,0000,,so that means I must also have the adjacent.
Dialogue: 0,0:01:08.27,0:01:12.06,Default,,0000,0000,0000,,Now, according to SOHCAHTOA,
Dialogue: 0,0:01:12.06,0:01:15.46,Default,,0000,0000,0000,,I need to use TOA,
Dialogue: 0,0:01:15.46,0:01:17.26,Default,,0000,0000,0000,,which is tan, of course,
Dialogue: 0,0:01:17.26,0:01:20.59,Default,,0000,0000,0000,,because I have O and A.
Dialogue: 0,0:01:20.66,0:01:22.95,Default,,0000,0000,0000,,That means that for me,
Dialogue: 0,0:01:22.95,0:01:27.66,Default,,0000,0000,0000,,tan of my angle equals,
Dialogue: 0,0:01:27.66,0:01:29.22,Default,,0000,0000,0000,,please make sure you're doing that equal sign.
Dialogue: 0,0:01:29.22,0:01:31.78,Default,,0000,0000,0000,,Otherwise, what you're writing doesn't actually make any sense.
Dialogue: 0,0:01:31.78,0:01:33.54,Default,,0000,0000,0000,,You also need to make sure you include
Dialogue: 0,0:01:33.54,0:01:36.32,Default,,0000,0000,0000,,this W because tan on its own doesn't mean anything.
Dialogue: 0,0:01:36.32,0:01:39.38,Default,,0000,0000,0000,,What this tells us is that tan of this angle,
Dialogue: 0,0:01:39.38,0:01:42.94,Default,,0000,0000,0000,,angle W is equal to 21.2 divided by 43.5.
Dialogue: 0,0:01:45.77,0:01:49.88,Default,,0000,0000,0000,,This tells us the ratio of these sides for this angle,
Dialogue: 0,0:01:49.88,0:01:51.52,Default,,0000,0000,0000,,and whatever this ratio is,
Dialogue: 0,0:01:51.52,0:01:53.56,Default,,0000,0000,0000,,there's only one possible angle that would fit.
Dialogue: 0,0:01:53.56,0:01:55.90,Default,,0000,0000,0000,,We're going to go ahead and solve that.
Dialogue: 0,0:01:55.90,0:01:58.100,Default,,0000,0000,0000,,Tan W equals,
Dialogue: 0,0:01:58.100,0:02:00.75,Default,,0000,0000,0000,,now, all we're doing here is dividing.
Dialogue: 0,0:02:00.75,0:02:02.98,Default,,0000,0000,0000,,I go ahead and divide,
Dialogue: 0,0:02:02.98,0:02:07.27,Default,,0000,0000,0000,,and I get 0.487356321,
Dialogue: 0,0:02:08.78,0:02:15.55,Default,,0000,0000,0000,,but I don't need all those decimal places.
Dialogue: 0,0:02:15.55,0:02:16.83,Default,,0000,0000,0000,,The rule that I've given you guys for
Dialogue: 0,0:02:16.83,0:02:20.06,Default,,0000,0000,0000,,this unit is to always round to four decimal places.
Dialogue: 0,0:02:20.06,0:02:23.03,Default,,0000,0000,0000,,The way that we do that, 1, 2, 3,
Dialogue: 0,0:02:23.03,0:02:26.47,Default,,0000,0000,0000,,4, and I look at the fifth decimal place.
Dialogue: 0,0:02:26.47,0:02:30.01,Default,,0000,0000,0000,,In this case, it's a five, and the rule is,
Dialogue: 0,0:02:30.01,0:02:31.63,Default,,0000,0000,0000,,if this is five or greater,
Dialogue: 0,0:02:31.63,0:02:34.16,Default,,0000,0000,0000,,it bumps up the one that came before it.
Dialogue: 0,0:02:34.16,0:02:37.74,Default,,0000,0000,0000,,This becomes a four,
Dialogue: 0,0:02:37.74,0:02:39.43,Default,,0000,0000,0000,,and we can ignore the rest of those.
Dialogue: 0,0:02:39.43,0:02:42.16,Default,,0000,0000,0000,,I'm just going to rewrite this so it's a little bit clear.
Dialogue: 0,0:02:42.16,0:02:47.68,Default,,0000,0000,0000,,Tan W equals 0.4874.
Dialogue: 0,0:02:49.08,0:02:51.26,Default,,0000,0000,0000,,Now, I can't just use
Dialogue: 0,0:02:51.26,0:02:54.56,Default,,0000,0000,0000,,the regular old tan button because I can only do that when I know the angle.
Dialogue: 0,0:02:54.56,0:02:56.24,Default,,0000,0000,0000,,When I'm trying to find the angle,
Dialogue: 0,0:02:56.24,0:02:58.58,Default,,0000,0000,0000,,I end up with something like this.
Dialogue: 0,0:02:58.58,0:03:02.80,Default,,0000,0000,0000,,Angle W equals inverse tan.
Dialogue: 0,0:03:02.80,0:03:05.50,Default,,0000,0000,0000,,Remember you hit the second button on your calculator
Dialogue: 0,0:03:05.50,0:03:08.39,Default,,0000,0000,0000,,or the shift button depending on how your calculator works.
Dialogue: 0,0:03:08.39,0:03:13.68,Default,,0000,0000,0000,,We're doing inverse tan of 0.4874.
Dialogue: 0,0:03:13.68,0:03:17.32,Default,,0000,0000,0000,,I go ahead and I type that in and I get the W
Dialogue: 0,0:03:17.32,0:03:26.60,Default,,0000,0000,0000,,equals 25.98 degrees or 26 degrees.
Dialogue: 0,0:03:28.00,0:03:30.82,Default,,0000,0000,0000,,By the way, the reason that color is changing is because
Dialogue: 0,0:03:30.82,0:03:32.90,Default,,0000,0000,0000,,I'm pausing it to use my calculator,
Dialogue: 0,0:03:32.90,0:03:34.78,Default,,0000,0000,0000,,and then when I turn it back on,
Dialogue: 0,0:03:34.78,0:03:37.28,Default,,0000,0000,0000,,it for some reason, puts something in black.
Dialogue: 0,0:03:37.28,0:03:40.44,Default,,0000,0000,0000,,You can just ignore that black and assume it's the same color.
Dialogue: 0,0:03:40.44,0:03:44.72,Default,,0000,0000,0000,,There's angle W. To find angle X, well, that's easy.
Dialogue: 0,0:03:44.72,0:03:48.56,Default,,0000,0000,0000,,Angle X, we know the angles all add up to 180,
Dialogue: 0,0:03:48.56,0:03:50.61,Default,,0000,0000,0000,,so it's 180-90,
Dialogue: 0,0:03:50.69,0:03:54.36,Default,,0000,0000,0000,,and then we subtract 26 degrees.
Dialogue: 0,0:03:54.36,0:03:59.01,Default,,0000,0000,0000,,180 minus 90 equals 90, 90 minus 20 is 70,
Dialogue: 0,0:03:59.01,0:04:05.88,Default,,0000,0000,0000,,take off another six and I believe it is 64 degrees.
Dialogue: 0,0:04:05.88,0:04:07.36,Default,,0000,0000,0000,,There we go. There's angle X.
Dialogue: 0,0:04:07.36,0:04:08.80,Default,,0000,0000,0000,,Now, I did that in my head,
Dialogue: 0,0:04:08.80,0:04:10.78,Default,,0000,0000,0000,,so I'm not really confident with that answer,
Dialogue: 0,0:04:10.78,0:04:13.66,Default,,0000,0000,0000,,so I'm not going to use that in my next calculation.
Dialogue: 0,0:04:13.66,0:04:15.98,Default,,0000,0000,0000,,I also already mentioned that I'm not going to use
Dialogue: 0,0:04:15.98,0:04:18.86,Default,,0000,0000,0000,,the Pythagorean theorem because I'd like to practice my trig a little bit more.
Dialogue: 0,0:04:18.86,0:04:24.18,Default,,0000,0000,0000,,I'm going to go ahead and use 26 degrees because I'm fairly confident in this answer.
Dialogue: 0,0:04:24.18,0:04:26.50,Default,,0000,0000,0000,,Now, some of you might want to use
Dialogue: 0,0:04:26.50,0:04:29.34,Default,,0000,0000,0000,,the Pythagorean theorem because you know that these numbers are correct,
Dialogue: 0,0:04:29.34,0:04:31.15,Default,,0000,0000,0000,,and if you use the Pythagorean theorem,
Dialogue: 0,0:04:31.15,0:04:35.62,Default,,0000,0000,0000,,you'll be certainly confident that your answer is correct, but I'm not going to.
Dialogue: 0,0:04:35.62,0:04:39.30,Default,,0000,0000,0000,,I'm going to use angle W as my reference angle,
Dialogue: 0,0:04:39.30,0:04:45.52,Default,,0000,0000,0000,,and the first thing I identify is that when I'm trying to find side Y,
Dialogue: 0,0:04:45.52,0:04:48.24,Default,,0000,0000,0000,,I'm looking for the hypotenuse.
Dialogue: 0,0:04:48.24,0:04:52.38,Default,,0000,0000,0000,,I know that I can either use sine because the hypotenuse is in there,
Dialogue: 0,0:04:52.38,0:04:53.98,Default,,0000,0000,0000,,or I can use cos.
Dialogue: 0,0:04:53.98,0:04:57.08,Default,,0000,0000,0000,,I can't use tan because the hypotenuse isn't involved,
Dialogue: 0,0:04:57.08,0:04:59.06,Default,,0000,0000,0000,,so it's not going to give me the hypotenuse.
Dialogue: 0,0:04:59.06,0:05:01.84,Default,,0000,0000,0000,,Now what I find is with angle W,
Dialogue: 0,0:05:01.84,0:05:04.96,Default,,0000,0000,0000,,I can either use 21.2,
Dialogue: 0,0:05:04.96,0:05:09.26,Default,,0000,0000,0000,,which is the opposite, or I can use 43.5, which is the adjacent.
Dialogue: 0,0:05:09.26,0:05:12.17,Default,,0000,0000,0000,,If I use 21.2,
Dialogue: 0,0:05:12.17,0:05:15.15,Default,,0000,0000,0000,,which is the opposite, I would use sine.
Dialogue: 0,0:05:15.15,0:05:17.49,Default,,0000,0000,0000,,If I use 43.5,
Dialogue: 0,0:05:17.49,0:05:20.66,Default,,0000,0000,0000,,which is the adjacent, I would use cos.
Dialogue: 0,0:05:20.66,0:05:22.61,Default,,0000,0000,0000,,Either way, I'll get the exact same answer.
Dialogue: 0,0:05:22.61,0:05:24.31,Default,,0000,0000,0000,,I haven't used cos yet, I don't think,
Dialogue: 0,0:05:24.31,0:05:28.35,Default,,0000,0000,0000,,so I'm going to use the adjacent side as well.
Dialogue: 0,0:05:28.70,0:05:32.06,Default,,0000,0000,0000,,A and H means I'm going to use cos,
Dialogue: 0,0:05:32.06,0:05:34.18,Default,,0000,0000,0000,,the adjacent always goes on top.
Dialogue: 0,0:05:34.18,0:05:36.53,Default,,0000,0000,0000,,Cos of my angle,
Dialogue: 0,0:05:36.53,0:05:46.07,Default,,0000,0000,0000,,which I decided was 26 degrees is equal to 43.5 over y.
Dialogue: 0,0:05:46.07,0:05:50.03,Default,,0000,0000,0000,,Now, what you'll notice is that in all three of these examples that I've done so far,
Dialogue: 0,0:05:50.03,0:05:52.29,Default,,0000,0000,0000,,or I guess both videos,
Dialogue: 0,0:05:52.29,0:05:54.81,Default,,0000,0000,0000,,my variable's been on the bottom, and that's the hard case.
Dialogue: 0,0:05:54.81,0:05:57.03,Default,,0000,0000,0000,,The easy case is when the variable's on top.
Dialogue: 0,0:05:57.03,0:05:58.83,Default,,0000,0000,0000,,Just remember, if your variable,
Dialogue: 0,0:05:58.83,0:06:00.97,Default,,0000,0000,0000,,that's the side you're solving for is on top,
Dialogue: 0,0:06:00.97,0:06:03.33,Default,,0000,0000,0000,,you're just going to multiply by what's underneath.
Dialogue: 0,0:06:03.33,0:06:08.91,Default,,0000,0000,0000,,It's only in these cases where the variable's on the bottom that you have to switch.
Dialogue: 0,0:06:08.91,0:06:11.82,Default,,0000,0000,0000,,Something that's helpful, if you look at SOHCAHTOA,
Dialogue: 0,0:06:11.82,0:06:13.96,Default,,0000,0000,0000,,if you're solving for the hypotenuse,
Dialogue: 0,0:06:13.96,0:06:16.54,Default,,0000,0000,0000,,it's on the bottom here and it's on the bottom here.
Dialogue: 0,0:06:16.54,0:06:18.30,Default,,0000,0000,0000,,Whenever you're solving for the hypotenuse,
Dialogue: 0,0:06:18.30,0:06:19.86,Default,,0000,0000,0000,,it's probably going to be on the bottom.
Dialogue: 0,0:06:19.86,0:06:21.88,Default,,0000,0000,0000,,If you're ever solving for the opposite,
Dialogue: 0,0:06:21.88,0:06:26.58,Default,,0000,0000,0000,,you can see it's on top, it's not involved, and it's on top.
Dialogue: 0,0:06:26.58,0:06:28.56,Default,,0000,0000,0000,,If you're solving for the opposite,
Dialogue: 0,0:06:28.56,0:06:32.10,Default,,0000,0000,0000,,it's always going to be on top, so it's always going to be the easier calculation.
Dialogue: 0,0:06:32.10,0:06:34.28,Default,,0000,0000,0000,,And if you're solving for the adjacent,
Dialogue: 0,0:06:34.28,0:06:38.76,Default,,0000,0000,0000,,it's either going to be on top with cos or it's going to be on the bottom with tan.
Dialogue: 0,0:06:38.76,0:06:40.98,Default,,0000,0000,0000,,If you like it being on top,
Dialogue: 0,0:06:40.98,0:06:43.72,Default,,0000,0000,0000,,use cos to find the adjacent,
Dialogue: 0,0:06:43.72,0:06:46.04,Default,,0000,0000,0000,,assuming, of course, that you have the hypotenuse.
Dialogue: 0,0:06:46.04,0:06:47.56,Default,,0000,0000,0000,,Let's finish this up.
Dialogue: 0,0:06:47.56,0:06:49.70,Default,,0000,0000,0000,,Again, we know that these two things switch,
Dialogue: 0,0:06:49.70,0:06:57.39,Default,,0000,0000,0000,,so we get y equals 43.5 divided by cos 26.
Dialogue: 0,0:06:57.39,0:06:58.44,Default,,0000,0000,0000,,We're solving for y,
Dialogue: 0,0:06:58.44,0:06:59.52,Default,,0000,0000,0000,,which is the hypotenuse,
Dialogue: 0,0:06:59.52,0:07:06.12,Default,,0000,0000,0000,,so we know that our answer has to be bigger than 43.5 and bigger than 21.2.
Dialogue: 0,0:07:06.12,0:07:08.83,Default,,0000,0000,0000,,I go ahead and I solve it,
Dialogue: 0,0:07:13.13,0:07:16.24,Default,,0000,0000,0000,,and I get 48.4,
Dialogue: 0,0:07:16.24,0:07:18.44,Default,,0000,0000,0000,,which is bigger than 43.5.
Dialogue: 0,0:07:18.44,0:07:23.06,Default,,0000,0000,0000,,I think that answer is probably correct. So 48.4 meters.
Dialogue: 0,0:07:23.06,0:07:27.03,Default,,0000,0000,0000,,Now I have solved this triangle.
Dialogue: 0,0:07:27.03,0:07:29.13,Default,,0000,0000,0000,,I have all the angles.
Dialogue: 0,0:07:29.13,0:07:31.50,Default,,0000,0000,0000,,I had two of the sides,
Dialogue: 0,0:07:31.50,0:07:32.78,Default,,0000,0000,0000,,and I found the third one.
Dialogue: 0,0:07:32.78,0:07:34.92,Default,,0000,0000,0000,,That is how I would go about solving this triangle,
Dialogue: 0,0:07:34.92,0:07:36.12,Default,,0000,0000,0000,,but as I mentioned in class,
Dialogue: 0,0:07:36.12,0:07:38.02,Default,,0000,0000,0000,,there are several ways to solve any of these,
Dialogue: 0,0:07:38.02,0:07:40.45,Default,,0000,0000,0000,,and the way that you do it is totally up to you.
Dialogue: 0,0:07:40.45,0:07:44.00,Default,,0000,0000,0000,,Good luck on the assignment, and I'll see you on Monday.