Open Middle: Creating Triangles

Move the number boxes on the left side to build a triangle with the given formatted side lengths. [br]Once you fill in all six boxes with number tiles, a triangle may (or may not) appear on the right side. [br][br]If a triangle [i]does[/i] appear on the right side, it will be built to scale.
Can you create an ACUTE triangle here? Try to do so!
In the space below, algebraically show (A) how you know this triangle even exists and (B) how you know this triangle is ACUTE.
Can you create an OBTUSE triangle here? Try to do so!
In the space below, algebraically show (A) how you know this triangle exists and (B) how you this triangle is OBTUSE.
Challenge: Can you create an RIGHT triangle here? Try to do so!
In the space below, algebraically show (A) how you know this triangle exists and (B) how you know this triangle is a RIGHT triangle.
– Tim Brzezinski

Information: Open Middle: Creating Triangles