Only 2% of people can solve this. Are you a genius? - By tecmath
Transcript
00:0-1 | Good day and welcome to the Tech mouth channel Problem | |
00:02 | I have for you today is we have a triangle | |
00:04 | . In fact , we have two triangles . We | |
00:05 | have a little triangle sitting inside a bigger triangle . | |
00:09 | We know the following . We know this little angle | |
00:11 | here is 20 degrees . We know this angle here | |
00:14 | is 80 degrees . We also know that this length | |
00:17 | here is equal to this length here . What we're | |
00:20 | trying to find and this is your challenge is can | |
00:23 | you find this unknown angle here ? Using only basic | |
00:27 | geometry ? You're not allowed to use trigonometry on this | |
00:29 | one ? You have to use basic geometry . So | |
00:32 | can you go about and do that Anyway , pause | |
00:34 | the video and see how you go and I'll come | |
00:37 | back with the answer . Okay , so time's up | |
00:53 | . Did you manage to solve it ? I'll tell | |
00:54 | you what , I'm going to go through how to | |
00:55 | work out this answer right now . So the first | |
00:58 | we're going to do is I'm going to label the | |
01:00 | different corners of this triangle just to help us with | |
01:04 | the explanation . So we have this corner here , | |
01:06 | I'm going to call a this corner here . I'm | |
01:08 | going to call be this corner here . I'm going | |
01:10 | to call C . And this part here , I'm | |
01:13 | going to call D where this intersection here occurs . | |
01:16 | So the first we're going to work out to solve | |
01:18 | this is what this angle is down here . We | |
01:20 | know that we have a triangle here and we have | |
01:23 | an angle of 80 and an angle of 20 . | |
01:26 | Now , angle A . B C . That is | |
01:28 | , this angle down here is going to equal 180 | |
01:32 | minus these two and also 180 degrees minus 80 degrees | |
01:38 | minus 20 degrees because in the entire of a triangle | |
01:41 | there is 180 degrees , so 180 minus 80 minus | |
01:46 | 20 is equal to 80 . So we know this | |
01:48 | angle down here is equal to 80 degrees . So | |
01:52 | what does this tell us if this angle here is | |
01:55 | 80 degrees and this angle here is 80 degrees . | |
01:57 | What this means is our triangle is an isosceles triangle | |
02:01 | . This triangle , A , B C . Is | |
02:05 | ice oscillates . That means we have to equal angles | |
02:08 | and on top of that we have to equal length | |
02:10 | here . So we can actually mark these on . | |
02:12 | I'm going to mark these two equal lengths on right | |
02:15 | now . We have this length here and we have | |
02:17 | this length here . The next thing we're going to | |
02:20 | do to solve this problem is we are going to | |
02:22 | draw an equilateral triangle that comes off this line here | |
02:25 | . An equilateral triangle has equal side lengths and equal | |
02:28 | angles . So an equilateral triangle would come out up | |
02:30 | here and it would go down to this park here | |
02:34 | . I'd had a side length here and these side | |
02:37 | length would be the same and this side length here | |
02:39 | would also be the same . Now we can also | |
02:41 | label the angles on our equilateral triangle here . We | |
02:44 | know that this angle up here , I'm going to | |
02:45 | call this E R . P . R . We | |
02:47 | know that this angle is going to be equal to | |
02:50 | 60 degrees because 180 divided by three is equal to | |
02:53 | 60 . We could work out this little part of | |
02:56 | the angle here because if this entire angle here is | |
02:59 | 60 degrees , well 60 take away 20 that would | |
03:03 | tell us that this angle here is 40 degrees . | |
03:06 | The last thing we're left with is this angle here | |
03:08 | , which is also 60 degrees . So the next | |
03:11 | thing we're going to work out is this angle here | |
03:14 | ? This angle E . B . C . Okay | |
03:17 | , I'll destroy it in there . Now , what | |
03:19 | do we know about this particular area ? We know | |
03:22 | that A . B . C . Is equal to | |
03:24 | 80 degrees . This entire angle here , we also | |
03:27 | know that on our collateral triangle this is equal to | |
03:31 | 60 degrees . So this little angle , this E | |
03:34 | B C is going to equal 80 degrees minus 60 | |
03:38 | degrees . So a t minus 60 . This is | |
03:41 | going to equal 20 degrees . All right . So | |
03:45 | let's get up to the next step . Now , | |
03:47 | we're going to draw a line between C and the | |
03:53 | and this gives us a triangle A C . E | |
03:56 | . Now , what do we know about triangle ? | |
03:58 | A . C . E . Well , we know | |
04:00 | it is also an isosceles triangle . What makes me | |
04:04 | say that ? Or we have this line here at | |
04:08 | this lawyer here Of equal length . So straight away | |
04:11 | this tells us we have an isosceles triangle . So | |
04:14 | now what we can do is we can work out | |
04:16 | a few of our unknown angles here , using this | |
04:19 | , what we know is this angle here and we | |
04:21 | work that out well , pretty simply right because we | |
04:24 | know this angle down here is 40°. . A triangle | |
04:28 | in total has 180°, , so we go 180° -40°. | |
04:34 | . And then we divide our result by two , | |
04:37 | dividing at least two angles here . It will tell | |
04:40 | us how big this angle here is . So 180 | |
04:43 | minus 40 is 100 and 40 divided by two . | |
04:47 | This angle is 70 degrees and we've almost solved this | |
04:51 | problem because what we've managed to create is two congruent | |
04:54 | triangles . That is to say two triangles that are | |
04:57 | similar in form . Okay , can you see where | |
05:00 | they are ? Okay , we're going to use information | |
05:03 | from one and transfer it across the other and use | |
05:05 | this to solve our problem . If you have a | |
05:07 | look at the first triangle here , we're going to | |
05:10 | have a look at the B . C . Okay | |
05:13 | , we have this length here and it has a | |
05:16 | 20 degree angle and this shorter length here . Okay | |
05:21 | . We have triangle the B . C . Can | |
05:24 | you spot the triangle that it is congruent to maybe | |
05:27 | you did . We have the long length from be | |
05:29 | going across A . We have this 20 degrees and | |
05:32 | then we have this shorter length here . It's going | |
05:34 | to be covered over there . So you might not | |
05:36 | have seen it where it goes off from A two | |
05:38 | D . Okay , so this is B . A | |
05:41 | . D . These two triangles are congruent one another | |
05:44 | there are identical . So we know this little angle | |
05:48 | here . We can find out what it is because | |
05:50 | we know it's the same as this angle here which | |
05:53 | is 80 Plus 70 . So what's 80 plus 70 | |
05:56 | , 80 plus 70 is equal to 150° in a | |
06:02 | straight line , there is 100 and 80 degrees . | |
06:04 | So we've got our final angle , our angle that | |
06:07 | we have to solve this is going to be equal | |
06:08 | to 180 degrees minus 150 degrees , which is equal | |
06:15 | to 30 degrees . And that is our answer . | |
06:18 | Our answer is 30 degrees . So how did you | |
06:22 | go ? Did you manage to solve this problem before | |
06:24 | me without using trigonometry ? If you did let us | |
06:26 | know in the comments below and if you like this | |
06:28 | video , please also let us know in the comments | |
06:30 | below and hit the like button and subscribe for more | |
06:33 | problems and our math tips and tricks to come along | |
06:36 | . Anyway , thank you for watching and we'll see | |
06:38 | you next time . Bye . |
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