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## Class 6

### Course: Class 6>Unit 7

Lesson 2: Properties of a triangle

# Triangle inequality theorem

Intuition behind the triangle inequality theorem. Created by Sal Khan.

## Want to join the conversation?

• What ways can you apply the Triangle Inqequality Theorem in real life?
• It can be used to determine bounds on distance.

For example, if I were at school and I knew that my home is 5 miles from school and my favorite fine dining establishment was 7 miles from school, I can conclude that the distance from my house to the restaurant is somewhere between 7-5=2 and 7+5=12.

It is a "large" range here, but still useful. A math teacher in my high school once mentioned to me that inequalities are far more useful than equalities in real life. Real life is not exact, so estimates that are good become extremely valuable.

Depending on how much math you have completed as a 10 year old, there are some topics in calculus that deal with bounding error on numerical approximations to definite integrals that are interesting and valuable and deal with uncertain (but bounded) answers.
• why didn't Sal maximize the angle to 360 degrees?
• so the range of "x" is the difference of the sides plus and minus the sides??
• Is it possible to figure out a triangle's full classification just using the triangle's sides, no angles or anything, just the lengths.
• Yes, By using sine, cosine, and tangent, we can figure out the angle measures.
• Could the angle be 0.00000000000001 or 179.9999999999999? Is that even possible or will it end up to be a degenerate traingle?
• Yes this is possible for a triangle. The triangle would not be degenerate, even though it’s nearly degenerate.

Any three interior angles that are positive and add to 180 degrees can form a non-degenerate triangle.
• What happens in the case of an isosceles triangle?
X > 0?
• when would we ever use this is in the real world unless for building or NASA?
• i agree
• What if the sum of two sides are equal to the side you didn't add?
• That is impossible. In order for that to happen, the triangle must turn into a straight line, which wouldn't be a triangle any more. The sum of two sides of a triangle will always be more than the other side, no matter what side you choose.

Hope this helps!
• im still confused can you explain it a little more please