This cannot be a 45-45-90 right triangle because we don't have congruent sides. This cannot be a 60-60-60 for the same reason.
For a 30-60-90 right triangle, the shorter leg has a length of x, the longer leg has a length of [tex]x \sqrt{3} [/tex], and the hypotenuse has a length of 2x.
Let's test this. Let [tex]x=7 \sqrt{3} [/tex]
Multiply that with [tex] \sqrt{3} [/tex]
[tex]7 \sqrt{3} * \sqrt{3} =21[/tex]
That matches the length of the longer leg.
Now, let's multiply x with 2 to see if it matches the length of the hypotenuse.
[tex]2x=7 \sqrt{3} *2=14 \sqrt{3} [/tex]
This matches the length of the hypotenuse. Thus, the angles are 30, 60, and 90 because this triangle is a 30-60-90 right triangle. Hope this helps! :)
