Shania and Pedro are discussing whether it is always possible to solve a right triangle, given enough information, without using the Pythagorean Theorem. Pedro says that it is always possible, but Shania thinks that when two side lengths and no angle measures are given, the Pythagorean Theorem is needed. Who is correct, and why?

Shania is correct.

Step-by-step explanation:

For a right angled triangle, given two sides and an angle, we can use the sine rule or the various trigonometry identities to solve the triangle;

a/sin A = b/sinB

and

sin (angle) = opposite side/hypotenuse

cos (angle) = adjacent side/hypotenuse

tan (angle) = opposite/ adjacent

assuming a is the opposite side of angle A and b is also opposite of angle B

Otherwise, the only way to solve a triangle given two sides only is by the use of the Pythagoras theorem.

Hence, Shania is correct.