Why is this not possible 30 60 90 right triangle problem?

Question

Answer 1

Since you posted this in Medicine, the answer is "see a doctor".

Answer 2

It does exist. a 5, 12, 13 is a Pythagorean triple.

It is a 30, 60, 90 or it is not a Pythagorean triple.

Answer 3

A 30-60-90 triangle has unique properties, these are not met in your problem. You should memorize this triangle.

Answer 4

In a 30-60-90 triangle, the side opposite the 30° divided by the hypotenuse, has to equal 0.5.  In this picture it is 5 / 13, which is not equal to 0.5.

A triangle with sides 5, 12, and 13 would have angles of 67.38°, 22.62°, and 90°.