The side-side-angle triangle is considered ambiguous because unlike the other triangles you first need to find the height of it and you can't just plug it right into a formula and figure out the answer. Also because there can be 2 solutions for this triangle, so by finding the height of it you can find out if you're just solving one triangle or 2.
To explain this law to someone who didn't have a lot of experience in math I would say that first you start out with 2 side of a triangle and one angle. From there you find the height of the triangle which you can do with a simple formula and plug in the angle you have , the side you have, and the side you need to find out which is the height. Then once you have the height you can figure out if it can be split into 2 triangles, if the the side opposite of the angle you have is bigger than the height it will make 2 triangles, if it's less than the height it will make none. You then solve each one of the trangles using formulas and find the different sides and angles for each one.
The diagram below shows that when you height you can find out if there's 2 triangles, 1 or 0. If the height is less than the right side then there are 2, if its the same as the height there is 1 triangle and if it's less than h there are 0.
To explain this law to someone who didn't have a lot of experience in math I would say that first you start out with 2 side of a triangle and one angle. From there you find the height of the triangle which you can do with a simple formula and plug in the angle you have , the side you have, and the side you need to find out which is the height. Then once you have the height you can figure out if it can be split into 2 triangles, if the the side opposite of the angle you have is bigger than the height it will make 2 triangles, if it's less than the height it will make none. You then solve each one of the trangles using formulas and find the different sides and angles for each one.
The diagram below shows that when you height you can find out if there's 2 triangles, 1 or 0. If the height is less than the right side then there are 2, if its the same as the height there is 1 triangle and if it's less than h there are 0.