Can you use the angle to figure out how long it actually is?

Not if you only know the three angles, you need at least one side. You can see this for yourself: draw a triangle on a piece of paper, it doesn't matter which angles you pick. Outside the triangle, next to each of the sides, draw another line parallel to the triangle's side. If you do this for all three sides, you'll get a second triangle which is bigger than the original, but has exactly the same angles. From that painting you can see that there is more than one triangle with exactly the same angles, but one is bigger than the other. In fact, there are infinitely many of such triangles! Once you know one side, you can use the law of sines to find the others. In case you're interested, here is the law of sines: a / sin(A) = b / sin(B) = c / sin(C) Where a is the length of one side and sin(A) the sine of the angle across from side a (and similar for b, B, c, and C).

Can we get accurate length of third side with the help of two sides

No, we can't, because although the length of the third side depends on the lengths of the other two sides it also depends on the angle between the two sides. However, if we had the two lengths and the angle, we could find the third side by using the law of cosines, which you can watch an example of here: https://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-law-of-cosines/v/law-of-cosines-example I don't know how familiar you are with the trigonometric functions, but the cosine function is one of them and they have in common that they make use of various relations between angles and sides in right triangles. If it's completely new to you, you can watch an introduction to trigonometry here: https://www.khanacademy.org/math/trigonometry/trigonometry-right-triangles/intro-to-the-trig-ratios/v/basic-trigonometry

can u tell me some tip how to order the smallest to largest? and from largest to smallest? i just need some clue please everyone!

I found it very well explained in the video. Really, what he's saying is that with only angles and not side lengths for any given triangle, the smallest interior angle (the one on the inside of the triangle) will have the largest once directly on the opposite side of the triangle.

are there more than just the common angles like acute, obtuse,and right?

Yes, there are many different types of angles, besides those three. There are straight, reflex,vertical, opposite, corresponding and 360 degree angles (just to name a few)

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Class 10 (Foundation)

Course: Class 10 (Foundation) > Unit 9

Lesson 5: Triangle inequalities

Ordering triangle sides and angles example

Name: Ordering triangle sides and angles example
Uploaded: 2016-01-18T15:19:10Z
Description: Sal first solves a problem where he orders the sides of a triangle given the angles, then solves a problem where he orders the angles of a triangle given the sides.

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Sal first solves a problem where he orders the sides of a triangle given the angles, then solves a problem where he orders the angles of a triangle given the sides.

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Jenny
Posted 7 years ago. Direct link to Jenny's post “Can you use the angle to ...”
Can you use the angle to figure out how long it actually is?
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(17 votes)
Answer
- ZeroFK
  Posted 7 years ago. Direct link to ZeroFK's post “Not if you only know the ...”
  Not if you only know the three angles, you need at least one side. You can see this for yourself: draw a triangle on a piece of paper, it doesn't matter which angles you pick. Outside the triangle, next to each of the sides, draw another line parallel to the triangle's side. If you do this for all three sides, you'll get a second triangle which is bigger than the original, but has exactly the same angles. From that painting you can see that there is more than one triangle with exactly the same angles, but one is bigger than the other. In fact, there are infinitely many of such triangles!
  
  Once you know one side, you can use the law of sines to find the others. In case you're interested, here is the law of sines:
  a / sin(A) = b / sin(B) = c / sin(C)
  Where a is the length of one side and sin(A) the sine of the angle across from side a (and similar for b, B, c, and C).
  Button navigates to signup page
  (5 votes)
Darlingdeerio
Posted 6 years ago. Direct link to Darlingdeerio's post “0:44 I don't get it. "The...”
0:44
I don't get it. "The side that this angle opens up to is going to be the shortest side of the triangle." I'm really stumped. What is the concepts of (The angle that this opens up to) and how is it always going to be the shortest side of the triangle if there's three?
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(5 votes)
Answer
- Raymond
  Posted 6 years ago. Direct link to Raymond's post “It's because the angle, 5...”
  It's because the angle, 57 degrees, is the smallest of the three angles.
  
  If you try increasing the angle measure, you'll notice that the opposite side will increase in length to compensate for the wider angle. Likewise, decreasing the angle will decrease the opposite side's length.
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  (0 votes)
😊
Posted 6 years ago. Direct link to 😊's post “Can we get accurate lengt...”
Can we get accurate length of third side with the help of two sides
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(2 votes)
Answer
- Jerry Nilsson
  Posted 6 years ago. Direct link to Jerry Nilsson's post “No, we can't, because alt...”
  No, we can't, because although the length of the third side depends on the lengths of the other two sides it also depends on the angle between the two sides.
  
  However, if we had the two lengths and the angle, we could find the third side by using the law of cosines, which you can watch an example of here:
  https://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-law-of-cosines/v/law-of-cosines-example
  
  I don't know how familiar you are with the trigonometric functions, but the cosine function is one of them and they have in common that they make use of various relations between angles and sides in right triangles.
  If it's completely new to you, you can watch an introduction to trigonometry here:
  https://www.khanacademy.org/math/trigonometry/trigonometry-right-triangles/intro-to-the-trig-ratios/v/basic-trigonometry
  Button navigates to signup page
  (5 votes)
Evelyn Cardriche
Posted 4 years ago. Direct link to Evelyn Cardriche's post “What is a good way to rem...”
What is a good way to remember the order?
Button navigates to signup pageComment on Evelyn Cardriche's post “What is a good way to rem...”
(3 votes)
Answer
🅸🅹🅱🅰🆄🆂🆄🅼
Posted 4 years ago. Direct link to 🅸🅹🅱🅰🆄🆂🆄🅼's post “At 0:54 sal says " the ne...”
At
0:54
sal says " the next largest angle"
But I think he meant to say " the next smallest angle"
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(3 votes)
Answer
kira mccluskey
Posted 6 years ago. Direct link to kira mccluskey's post “why are some triangles so...”
why are some triangles so confusing sometimes.
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(3 votes)
Answer
Youpanhamorakath123
Posted 6 years ago. Direct link to Youpanhamorakath123's post “in the first video he say...”
in the first video he say they have given the interior angels of the triangle what that mean?
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(2 votes)
Answer
- Afriasia Bermúdez-Crespín
  Posted 6 years ago. Direct link to Afriasia Bermúdez-Crespín's post “The angle measures on the...”
  The angle measures on the inside of the triangle. Hope this helps!
  Button navigates to signup page
  (1 vote)
Youpanhamorakath123
Posted 6 years ago. Direct link to Youpanhamorakath123's post “can u tell me some tip ho...”
can u tell me some tip how to order the smallest to largest?
and from largest to smallest?
i just need some clue please everyone!
Button navigates to signup pageButton navigates to signup page
(1 vote)
Answer
- cal gotz
  Posted 6 years ago. Direct link to cal gotz's post “I found it very well expl...”
  I found it very well explained in the video.
  Really, what he's saying is that with only angles and not side lengths for any given triangle, the smallest interior angle (the one on the inside of the triangle) will have the largest once directly on the opposite side of the triangle.
  Button navigates to signup page
  (2 votes)
Cordova Joaquin
Posted 5 years ago. Direct link to Cordova Joaquin's post “are there more than just ...”
are there more than just the common angles like acute, obtuse,and right?
Button navigates to signup pageComment on Cordova Joaquin's post “are there more than just ...”
(1 vote)
Answer
- REAL NAME
  Posted 5 years ago. Direct link to REAL NAME's post “Yes, there are many diffe...”
  Yes, there are many different types of angles, besides those three. There are straight, reflex,vertical, opposite, corresponding and 360 degree angles (just to name a few)
  Button navigates to signup page
  (2 votes)
NEKO#ΦωΦ
Posted 3 years ago. Direct link to NEKO#ΦωΦ's post “so if I just type in som...”
so if I just type in some numbers they would turn blu
0:78
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(1 vote)
Answer
- brianzenghs
  Posted 3 years ago. Direct link to brianzenghs's post “The blue number is nothin...”
  The blue number is nothing more than the time on the video. 0:78 is impossible as after 60 seconds it turns into
  1:01
  .
  Button navigates to signup page
  (1 vote)

Video transcript

- [Voiceover] We're asked to order the side lengths of the triangle from shortest to longest. And we have the three sides here, and we could use this little tool to order them in some way. If we look at the triangle, we've been given the interior angles of the triangle, and they haven't told us the actual side lengths. So, how are we supposed to actually order them from shortest to longest? Well, the realization that you need to make here is that the order of the lengths of the sides of a triangle are related to the order of the measures of angles that open up onto those sides. What do I mean by that? Well, let's think about these three angles right over here. 57 degrees, that is the smallest of these three, and so the side that this angle opens up to, or you can think of it as the opposite side, is going to be the shortest side of the triangle. So, b is going to be the shortest side. So, the next largest angle is 58 degrees, and so a is going to be the middle side. It's not going to be the longest nor the shortest. So, a. Then 65 degrees, that opens up onto side c, or the opposite side of that angle is c. So, c is going to be the longest side. To get an intuition for why that is, imagine a world where the 65 degree angle, if we were to make it bigger. If we were to make the 65 degree angle bigger, maybe by moving this point out and that point out, what would happen? Well, side c would get bigger, and because the angles of a triangle have to add up to 180 degrees, if this one's getting bigger, these will have to get smaller. Likewise, if I were to take angle... let's say, if I were to take this 58 degree angle, and if I were to make it smaller, what's going to happen? Well, side a is going to get smaller. So, the general principle, I'm not giving you any formal proof here, but the intuition is, is that the order of the angles will tell you what the order of the sides are going to be. So, the smallest side is going to be opposite the smallest angle. The largest side is going to be opposite the largest angle. We can check our answer, make sure we got it right. Now, let's do one that goes the other way around. Here, we want to order the angles of the triangle from smallest to largest, and we're given the sides. Well, same, exact idea. The smallest angle is going to be opposite the smallest side or the shortest side. Well, the shortest side is this side of length 7.2. The angle that opens up onto it is angle a. So, that's going to be the smallest angle. Then, the next smallest side is the side of length 7.3, and the angle that opens up to it is angle b right over here. So, angle b. Then angle c opens up onto the largest side. So, it's going to be the largest angle. So, we're done. We've ordered the angles of the triangle from smallest to largest.