Question

PTG has side lengths of 12 cm, 25 cm, and 19 cm. Which type of triangle is PTG?

Answer 1

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.