1 00:00:02,360 --> 00:00:04,840 INSTRUCTOR: Hello again, Grade Elevens. 2 00:00:04,840 --> 00:00:08,080 I'm just going to run you through one more example of solving a triangle. 3 00:00:08,080 --> 00:00:12,080 The difference with this one is that we are given the lengths of two sides, 4 00:00:12,080 --> 00:00:14,100 and in this case, we have no angles. 5 00:00:14,100 --> 00:00:16,400 I would probably say that most of you, 6 00:00:16,400 --> 00:00:20,660 the first thing that you're going to want to do is to find side y here, 7 00:00:20,660 --> 00:00:24,440 and the way that you're going to do that probably is to use the Pythagorean theorem. 8 00:00:24,440 --> 00:00:26,360 That's great. It would certainly work. 9 00:00:26,360 --> 00:00:28,880 I'm not going to use the Pythagorean theorem because for me, 10 00:00:28,880 --> 00:00:31,025 I think that trig works a little bit better. 11 00:00:31,025 --> 00:00:32,780 Well, it doesn't work better, it works the same, 12 00:00:32,780 --> 00:00:34,910 but I do think it's a little bit quicker. 13 00:00:34,910 --> 00:00:38,170 First, I have to find the angles. 14 00:00:38,170 --> 00:00:41,015 I have no choice. I have to use trig at least once. 15 00:00:41,015 --> 00:00:43,330 I'm going to find angle W first. 16 00:00:43,330 --> 00:00:49,350 What I have to do to do this is recognize that W becomes my reference angle, 17 00:00:49,350 --> 00:00:52,490 and now I have to take a look at what information I have. 18 00:00:52,490 --> 00:00:56,830 I'm looking for the angle, which means I need to have two sides. 19 00:00:57,190 --> 00:01:02,335 I come across from W and I recognize that I have the opposite side. 20 00:01:02,335 --> 00:01:04,670 I obviously don't have the hypotenuse yet, 21 00:01:04,670 --> 00:01:08,270 so that means I must also have the adjacent. 22 00:01:08,270 --> 00:01:12,060 Now, according to SOHCAHTOA, 23 00:01:12,060 --> 00:01:15,465 I need to use TOA, 24 00:01:15,465 --> 00:01:17,265 which is tan, of course, 25 00:01:17,265 --> 00:01:20,590 because I have O and A. 26 00:01:20,660 --> 00:01:22,950 That means that for me, 27 00:01:22,950 --> 00:01:27,660 tan of my angle equals, 28 00:01:27,660 --> 00:01:29,220 please make sure you're doing that equal sign. 29 00:01:29,220 --> 00:01:31,780 Otherwise, what you're writing doesn't actually make any sense. 30 00:01:31,780 --> 00:01:33,540 You also need to make sure you include 31 00:01:33,540 --> 00:01:36,320 this W because tan on its own doesn't mean anything. 32 00:01:36,320 --> 00:01:39,380 What this tells us is that tan of this angle, 33 00:01:39,380 --> 00:01:42,940 angle W is equal to 21.2 divided by 43.5. 34 00:01:45,770 --> 00:01:49,885 This tells us the ratio of these sides for this angle, 35 00:01:49,885 --> 00:01:51,520 and whatever this ratio is, 36 00:01:51,520 --> 00:01:53,560 there's only one possible angle that would fit. 37 00:01:53,560 --> 00:01:55,905 We're going to go ahead and solve that. 38 00:01:55,905 --> 00:01:58,995 Tan W equals, 39 00:01:58,995 --> 00:02:00,750 now, all we're doing here is dividing. 40 00:02:00,750 --> 00:02:02,985 I go ahead and divide, 41 00:02:02,985 --> 00:02:07,270 and I get 0.487356321, 42 00:02:08,780 --> 00:02:15,550 but I don't need all those decimal places. 43 00:02:15,550 --> 00:02:16,830 The rule that I've given you guys for 44 00:02:16,830 --> 00:02:20,060 this unit is to always round to four decimal places. 45 00:02:20,060 --> 00:02:23,030 The way that we do that, 1, 2, 3, 46 00:02:23,030 --> 00:02:26,470 4, and I look at the fifth decimal place. 47 00:02:26,470 --> 00:02:30,010 In this case, it's a five, and the rule is, 48 00:02:30,010 --> 00:02:31,630 if this is five or greater, 49 00:02:31,630 --> 00:02:34,155 it bumps up the one that came before it. 50 00:02:34,155 --> 00:02:37,740 This becomes a four, 51 00:02:37,740 --> 00:02:39,430 and we can ignore the rest of those. 52 00:02:39,430 --> 00:02:42,155 I'm just going to rewrite this so it's a little bit clear. 53 00:02:42,155 --> 00:02:47,680 Tan W equals 0.4874. 54 00:02:49,080 --> 00:02:51,260 Now, I can't just use 55 00:02:51,260 --> 00:02:54,560 the regular old tan button because I can only do that when I know the angle. 56 00:02:54,560 --> 00:02:56,240 When I'm trying to find the angle, 57 00:02:56,240 --> 00:02:58,575 I end up with something like this. 58 00:02:58,575 --> 00:03:02,795 Angle W equals inverse tan. 59 00:03:02,795 --> 00:03:05,500 Remember you hit the second button on your calculator 60 00:03:05,500 --> 00:03:08,390 or the shift button depending on how your calculator works. 61 00:03:08,390 --> 00:03:13,685 We're doing inverse tan of 0.4874. 62 00:03:13,685 --> 00:03:17,325 I go ahead and I type that in and I get the W 63 00:03:17,325 --> 00:03:26,600 equals 25.98 degrees or 26 degrees. 64 00:03:28,000 --> 00:03:30,820 By the way, the reason that color is changing is because 65 00:03:30,820 --> 00:03:32,900 I'm pausing it to use my calculator, 66 00:03:32,900 --> 00:03:34,780 and then when I turn it back on, 67 00:03:34,780 --> 00:03:37,280 it for some reason, puts something in black. 68 00:03:37,280 --> 00:03:40,440 You can just ignore that black and assume it's the same color. 69 00:03:40,440 --> 00:03:44,715 There's angle W. To find angle X, well, that's easy. 70 00:03:44,715 --> 00:03:48,560 Angle X, we know the angles all add up to 180, 71 00:03:48,560 --> 00:03:50,610 so it's 180-90, 72 00:03:50,690 --> 00:03:54,360 and then we subtract 26 degrees. 73 00:03:54,360 --> 00:03:59,010 180 minus 90 equals 90, 90 minus 20 is 70, 74 00:03:59,010 --> 00:04:05,880 take off another six and I believe it is 64 degrees. 75 00:04:05,880 --> 00:04:07,360 There we go. There's angle X. 76 00:04:07,360 --> 00:04:08,800 Now, I did that in my head, 77 00:04:08,800 --> 00:04:10,780 so I'm not really confident with that answer, 78 00:04:10,780 --> 00:04:13,660 so I'm not going to use that in my next calculation. 79 00:04:13,660 --> 00:04:15,980 I also already mentioned that I'm not going to use 80 00:04:15,980 --> 00:04:18,860 the Pythagorean theorem because I'd like to practice my trig a little bit more. 81 00:04:18,860 --> 00:04:24,180 I'm going to go ahead and use 26 degrees because I'm fairly confident in this answer. 82 00:04:24,180 --> 00:04:26,500 Now, some of you might want to use 83 00:04:26,500 --> 00:04:29,340 the Pythagorean theorem because you know that these numbers are correct, 84 00:04:29,340 --> 00:04:31,150 and if you use the Pythagorean theorem, 85 00:04:31,150 --> 00:04:35,620 you'll be certainly confident that your answer is correct, but I'm not going to. 86 00:04:35,620 --> 00:04:39,300 I'm going to use angle W as my reference angle, 87 00:04:39,300 --> 00:04:45,520 and the first thing I identify is that when I'm trying to find side Y, 88 00:04:45,520 --> 00:04:48,245 I'm looking for the hypotenuse. 89 00:04:48,245 --> 00:04:52,380 I know that I can either use sine because the hypotenuse is in there, 90 00:04:52,380 --> 00:04:53,980 or I can use cos. 91 00:04:53,980 --> 00:04:57,080 I can't use tan because the hypotenuse isn't involved, 92 00:04:57,080 --> 00:04:59,065 so it's not going to give me the hypotenuse. 93 00:04:59,065 --> 00:05:01,840 Now what I find is with angle W, 94 00:05:01,840 --> 00:05:04,960 I can either use 21.2, 95 00:05:04,960 --> 00:05:09,265 which is the opposite, or I can use 43.5, which is the adjacent. 96 00:05:09,265 --> 00:05:12,170 If I use 21.2, 97 00:05:12,170 --> 00:05:15,150 which is the opposite, I would use sine. 98 00:05:15,150 --> 00:05:17,490 If I use 43.5, 99 00:05:17,490 --> 00:05:20,665 which is the adjacent, I would use cos. 100 00:05:20,665 --> 00:05:22,610 Either way, I'll get the exact same answer. 101 00:05:22,610 --> 00:05:24,310 I haven't used cos yet, I don't think, 102 00:05:24,310 --> 00:05:28,350 so I'm going to use the adjacent side as well. 103 00:05:28,700 --> 00:05:32,055 A and H means I'm going to use cos, 104 00:05:32,055 --> 00:05:34,185 the adjacent always goes on top. 105 00:05:34,185 --> 00:05:36,530 Cos of my angle, 106 00:05:36,530 --> 00:05:46,070 which I decided was 26 degrees is equal to 43.5 over y. 107 00:05:46,070 --> 00:05:50,030 Now, what you'll notice is that in all three of these examples that I've done so far, 108 00:05:50,030 --> 00:05:52,290 or I guess both videos, 109 00:05:52,290 --> 00:05:54,810 my variable's been on the bottom, and that's the hard case. 110 00:05:54,810 --> 00:05:57,030 The easy case is when the variable's on top. 111 00:05:57,030 --> 00:05:58,830 Just remember, if your variable, 112 00:05:58,830 --> 00:06:00,970 that's the side you're solving for is on top, 113 00:06:00,970 --> 00:06:03,330 you're just going to multiply by what's underneath. 114 00:06:03,330 --> 00:06:08,910 It's only in these cases where the variable's on the bottom that you have to switch. 115 00:06:08,910 --> 00:06:11,820 Something that's helpful, if you look at SOHCAHTOA, 116 00:06:11,820 --> 00:06:13,960 if you're solving for the hypotenuse, 117 00:06:13,960 --> 00:06:16,545 it's on the bottom here and it's on the bottom here. 118 00:06:16,545 --> 00:06:18,305 Whenever you're solving for the hypotenuse, 119 00:06:18,305 --> 00:06:19,860 it's probably going to be on the bottom. 120 00:06:19,860 --> 00:06:21,880 If you're ever solving for the opposite, 121 00:06:21,880 --> 00:06:26,580 you can see it's on top, it's not involved, and it's on top. 122 00:06:26,580 --> 00:06:28,560 If you're solving for the opposite, 123 00:06:28,560 --> 00:06:32,100 it's always going to be on top, so it's always going to be the easier calculation. 124 00:06:32,100 --> 00:06:34,280 And if you're solving for the adjacent, 125 00:06:34,280 --> 00:06:38,765 it's either going to be on top with cos or it's going to be on the bottom with tan. 126 00:06:38,765 --> 00:06:40,980 If you like it being on top, 127 00:06:40,980 --> 00:06:43,720 use cos to find the adjacent, 128 00:06:43,720 --> 00:06:46,040 assuming, of course, that you have the hypotenuse. 129 00:06:46,040 --> 00:06:47,560 Let's finish this up. 130 00:06:47,560 --> 00:06:49,700 Again, we know that these two things switch, 131 00:06:49,700 --> 00:06:57,390 so we get y equals 43.5 divided by cos 26. 132 00:06:57,390 --> 00:06:58,440 We're solving for y, 133 00:06:58,440 --> 00:06:59,520 which is the hypotenuse, 134 00:06:59,520 --> 00:07:06,125 so we know that our answer has to be bigger than 43.5 and bigger than 21.2. 135 00:07:06,125 --> 00:07:08,830 I go ahead and I solve it, 136 00:07:13,130 --> 00:07:16,245 and I get 48.4, 137 00:07:16,245 --> 00:07:18,435 which is bigger than 43.5. 138 00:07:18,435 --> 00:07:23,055 I think that answer is probably correct. So 48.4 meters. 139 00:07:23,055 --> 00:07:27,030 Now I have solved this triangle. 140 00:07:27,030 --> 00:07:29,130 I have all the angles. 141 00:07:29,130 --> 00:07:31,500 I had two of the sides, 142 00:07:31,500 --> 00:07:32,775 and I found the third one. 143 00:07:32,775 --> 00:07:34,920 That is how I would go about solving this triangle, 144 00:07:34,920 --> 00:07:36,120 but as I mentioned in class, 145 00:07:36,120 --> 00:07:38,020 there are several ways to solve any of these, 146 00:07:38,020 --> 00:07:40,450 and the way that you do it is totally up to you. 147 00:07:40,450 --> 00:07:44,000 Good luck on the assignment, and I'll see you on Monday.