Are these right triangles?
Solution:
We can use the Converse of the Pythagorean Theorem to find if the triangles are right triangles.
If the equation a^{2}+b^{2}=c^{2} is true, then we will have a right triangle.
For the first triangle:

a^{2}+b^{2}=c^{2}
12^{2}+35^{2}=36^{2}
The first triangle is not a right triangle. 
For the second triangle:

a^{2}+b^{2}=c^{2}
15^{2}+36^{2}=39^{2}
1521=1521
The second triangle is a right triangle 