Answer:
It is not a right triangles because 15^2 + 13^2 is NOT EQUAL to 19^2
let x, y, and z be the angles inside the triangle.
Law of cosines says:
19^2 = 13^2 + 15^2 - 2(13)(15)cos x
361 = 169 + 225 - 390 cos x
-33 = -390 cos x
-33/-390 = cos x
11/130 = cos x
x = inverse cosine (11/130)
= 85.14609471338569.....
Per law of sines:
sin x/19 = sin y / 13
(13/19)sinx = sin y
inverse_sine ( (13/19) sin x) = y
y = 42.9810733896016548....
Per law of sines
sin x/19 = sin z / 15
z = inverse_sine( (15/19) sin x)
= 51.8728352950227805....
So it is an acute triangle and yes, these angles add up to 180
