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### Course: Geometric Measurement & Modeling 221-230>Unit 2

Lesson 3: Inequalities in a triangle

# Ordering triangle sides and angles example

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.

## Want to join the conversation?

• 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
• 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?
• 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.
• What is a good way to remember the order?
• At sal says " the next largest angle"
But I think he meant to say " the next smallest angle"
• why are some triangles so confusing sometimes.
• in the first video he say they have given the interior angels of the triangle what that mean?
• The angle measures on the inside of the triangle. Hope this helps!
• 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.