Ptg has side lengths of 12 cm, 25 cm, and 19 cm. which type of triangle is ptg?

right

acute

obtuse

isosceles

No two sides are equal, so the triangle is not an isosceles triangle.

We could calculate at least two angles of the triangle to determine whether it is a right, acute, or obtuse. We need to use the cosine law:

a^2 + b^2 - 2ab * cos C = c^2
cos C = (a^2 + b^2 - c^2) / 2ab
C = arccos((a^2 + b^2 - c^2) / 2ab)

Solving for two angles P and T,

P = arccos((12^2 + 19^2 - 25^2)/(2*12*19))
P = 105.3 degrees.

Since one angle is an obtuse angle, we dont need to compute for the other angle. We can conclude then that the triangle is an obtuse angle.