Both pythagorean theorem and trigonometric ratios are used with right triangles. explain what information you need to apply to these different methods and include examples to show how to use each.

If given the value of an angle of the right triangle (aside from the 90° angle), then the trigonometric ratios will be more useful for solving for the sides of the triangle. One could use sin, cosin, and tangeant, the main trigonmetric ratios to solve for all sides and angles of the triangle, if given at least one angle and one side length. 

The Pythagorean Theorem as it is generally applied, helps solve for the third side of a triangle, given that you know the other 2 sides. This is less applicable, and trigonometric ratios can also be used in this case to solve for the rest of the triangle's angles and the third side.