Sin Cos and Tan - Basic Trigonometry Example - By tecmath
Transcript
| 00:03 | Okay , for the example of trigonometry I have here | |
| 00:06 | , I'm going to be dealing with a roof . | |
| 00:08 | Okay , because it's a nice example which you may | |
| 00:12 | probably use in the future . Okay , well this | |
| 00:16 | roof , it spans 5200 . It also has these | |
| 00:20 | eave overhangs on each side of 600 . This roof | |
| 00:25 | has a pitch of 23°. . So things which we're | |
| 00:28 | going to be wanting to find out with this room | |
| 00:31 | . First off , it's going to be height that | |
| 00:34 | this roof goes to . So draw a little triangle | |
| 00:37 | which deals with this triangle from there to their just | |
| 00:42 | a very approximate sort of triangle . Okay then , | |
| 00:46 | I'll move this . Okay , This will be the | |
| 00:47 | first triangle we're going to deal with . Okay . | |
| 00:55 | That it has the height that we're trying to find | |
| 01:01 | . In addition we have to work , we know | |
| 01:03 | the actual air at the length down here . It's | |
| 01:06 | going to be half of how much this roof actually | |
| 01:08 | spans . So 5200 divided by two is 2000 600 | |
| 01:15 | . Okay , that will be the first thing we're | |
| 01:16 | trying to find out , the next thing we're going | |
| 01:18 | to try and find out is this rafter length there | |
| 01:23 | ? Okay , this is a right angle triangle . | |
| 01:31 | Yeah , with this right angle triangle , it will | |
| 01:34 | be a little bit different in its dimensions from the | |
| 01:37 | last one we drew . And I'll show you how | |
| 01:39 | in just a second , I'll move it first , | |
| 01:43 | we'll move it down to here where we'll deal with | |
| 01:45 | that second as well . Okay , The dimensions of | |
| 01:49 | this , as I said , a slightly different angle | |
| 01:51 | here is the same 23° in the pitch . This | |
| 01:54 | is the length . We're trying to find this one | |
| 01:57 | down . The bottom here is going to be slightly | |
| 01:59 | different because this time it includes , it has to | |
| 02:02 | take into account the eaves . Okay , the rafter | |
| 02:05 | actually runs down right over the eaves . So I | |
| 02:07 | have to include this 600,000,000 2600 plus 600 3000 200 | |
| 02:16 | . Okay , cool . So these are the two | |
| 02:19 | things we're going to find . As you may remember | |
| 02:22 | from the last video we had on trigonometry , there | |
| 02:25 | was a couple of things we have to do . | |
| 02:27 | The first thing to do was labeled asides . The | |
| 02:30 | next thing we have to do . I was working | |
| 02:33 | at the trig function that was sign because what time | |
| 02:42 | then we had to substitute in values . Obviously it | |
| 02:46 | nice and short while I'm writing here and then we | |
| 02:51 | have to calculate , you know the way that we | |
| 02:54 | label decides if you remember the side opposite . The | |
| 02:59 | actual angle here was known as the opposite . So | |
| 03:02 | I'll just put that in the officer alongside the high | |
| 03:06 | pot news . We're not using that , but we're | |
| 03:08 | dealing with the adjacent . Okay . So a label | |
| 03:12 | decides for this one here . Then we have to | |
| 03:15 | work out whether we're using sign cause or tan . | |
| 03:17 | I had my way of remembering this with some old | |
| 03:20 | hags . We can't always act . They're old . | |
| 03:27 | Yeah . Right now we're going to be looking for | |
| 03:30 | the function but uses both the opposite and the adjacent | |
| 03:37 | so that this one is going to be tanned . | |
| 03:41 | So I'll write that down . Tan feeder equals the | |
| 03:46 | opposite over the adjacent . Remember feta is the angle | |
| 03:50 | . So I'll rewrite this out by substituting the values | |
| 03:54 | 10 ft are tan 23 degrees equals the opposite the | |
| 04:00 | opposite . Exa Yeah . And the adjacent is 2000 | |
| 04:06 | 600 . All right . In the last video also | |
| 04:11 | showed you how I now work . What exes . | |
| 04:15 | Okay . The way I would do that as I | |
| 04:18 | would write out this thing which I wrote in the | |
| 04:20 | last video . Three legal 6/2 . Now , if | |
| 04:22 | you're not sure this step , you may want to | |
| 04:24 | review the last video . Okay . But for the | |
| 04:28 | people who have done this , if we're looking XIA | |
| 04:32 | X lines up with the six here , Okay , | |
| 04:34 | What would I do two and three to get six | |
| 04:37 | times . So X is going to be These two | |
| 04:40 | times . So these two here and two times 10 | |
| 04:47 | , Time to 2600 and they're equals , he's my | |
| 04:53 | calculator 23 . 10 times 2 , 600 equals 11 | |
| 05:05 | oh three , rounded up to 114 . Actually , | |
| 05:09 | I'll do that now . 114 No matter . So | |
| 05:16 | , that's the hard work there . The next thing | |
| 05:20 | I was working at was the rafter . Okay . | |
| 05:23 | So I've got my triangle down here again . The | |
| 05:27 | first thing I do is label the sides . All | |
| 05:29 | right . So , we're not dealing with the opposite | |
| 05:32 | here . We're going to be dealing with the high | |
| 05:33 | pot news and the adjacent . The next thing I | |
| 05:36 | had to do was work out the economic function . | |
| 05:38 | Okay . The one that deals with I am , | |
| 05:42 | which is because okay . So rather than cause freedom | |
| 05:48 | equals a over age . Okay . We're going to | |
| 05:55 | continue this deadly actually cause 23 degrees because the adjacent | |
| 06:03 | , Which is 3000 200 over the high point news | |
| 06:10 | . Which is why . Okay , I'll write my | |
| 06:12 | three equals six over to We're dealing with . We're | |
| 06:18 | trying to find out the one here . Why ? | |
| 06:21 | Why this one here ? What we do is six | |
| 06:25 | and three is we have to go six divided by | |
| 06:27 | three . So we're going to go 3200 divided by | |
| 06:30 | customers . 3200 divided by cause 23 equals calculator . | |
| 06:42 | 3200 provided by 23 Cause who ? That doesn't look | |
| 06:51 | very good . Better hit eagle . That's much better | |
| 06:56 | . 3476 34 Soon six millimeters . Okay , so | |
| 07:08 | that's going to be the rifle leaf . Just we | |
| 07:11 | have 3.5 million . Okay , that's all pretty good | |
| 07:14 | . Last thing which we can also do here is | |
| 07:16 | we can work out this little angle up here and | |
| 07:19 | I'll show you quickly how to do that . Just | |
| 07:21 | a bit of information . So This angle here is | |
| 07:24 | 90°. . This angle here , 23°. . All angles | |
| 07:30 | in a triangle add up to 100 80 degrees . | |
| 07:34 | So 90 plus 123 . 130 . We take that | |
| 07:39 | away from 180 we get the answer for 67°. . | |
| 07:43 | This angle up here is going to be 67° anyway | |
| 07:47 | . That's where trigonometry can be used in the real | |
| 07:49 | world . And that's an example . Hope helps you | |
| 07:52 | understand trigonometry that little bit better . Okay , we'll | |
| 07:55 | see you next time . Bye . |
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Sin Cos and Tan - Basic Trigonometry Example is a free educational video by tecmath.
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