Trig Problem need someone to explain this

[Dantes]

Given 2 angles of a triangle, how many triangles are possible? Explain why.

Seeing how a triangle is 180 degrees, and if they give you two angles, that automatically locks the 3rd one at a certain value that will equal 180 when added with the other 2 angles. So I get 1.

My other idea was that it was infinity since you can divide the triangle with the two given sides into infinite smaller pieces as you get smaller and smaller.

I also think I might be missing a big point which is taking into consideration the sides of the triangle.

Any help would be very appreciated.

 

[Damned charming :)]

Given 2 angles you can automatically get the third angle. So the angles and shape are fixed. However you can double each side and get the same shape. You could also triple the size, or as you say shrink the size etc. So their are an infinite number of triangles of different size but the same shape. The formal name for triangle with two equal sides is " similar triangles". The only slightly tricky thing in this area that your teachers may be ruthless is that if that given two sides and an the non-included angle you can make actually make two triangles. People ignore the fact that if the non included angle is greater than 90 degrees

 

[tacman]

There are actually an infinite number of triangles that are possible with two given angles. This is because the length of the sides of the triangle can vary, as long as the two given angles remain constant. As you mentioned, you can divide the triangle into smaller and smaller pieces, creating an infinite number of triangles. Each triangle will have a different combination of side lengths, but as long as the two given angles remain the same, they will all have the same overall shape.

Another way to think about it is that the two given angles determine the measure of the third angle, but the length of the sides can vary. So even if you have two triangles with the same two given angles, they can have different side lengths and therefore be different triangles.

It is important to consider the sides of the triangle because they are what give the triangle its unique properties and shape. Without taking into account the side lengths, we cannot accurately determine the number of possible triangles.

In summary, there are an infinite number of triangles possible with two given angles because the length of the sides can vary while the two given angles remain constant. The sides of the triangle are an important factor in determining the number of possible triangles.