Question

A triangle has the following measurements. What is a possible length for the third side?

GH = 19, HJ = 8, JG = ?

Answer 1

the third side should be between 19-8 and 19+8

Answer 2

Picture two sides of a triangle, and imagine making the angle between them wider and wider.

What's happening as that angle gets wider? Well, you can see that, if we were to draw the third side, it's longer and longer as we make the angle wider. But what happens? Is there any limit to how long we can make that third side?

Well, the angle can't be as wide as 180, or there would be no triangle, but just a straight line. So that means that 180 degrees is the limit on the wideness of that angle, which means the the length of the third side is limited to being less than the straight line that would be formed if it was 180.

Answer 3

There's also a limit on how SHORT the third side could be, as Avinish pointed out. Imagine making the angle narrower and narrower. What happens? What is the limit on how small we can make that third side?

The angle has to be bigger than 0, so the third side has to be bigger than 19-8