The Hypotenuse-Leg (HL) theorem states that if the hypotenuse and one corresponding leg of a right triangle are equal to the hypotenuse and one corresponding leg of another right triangle, then the two triangles are congruent.
In your case, you stated that triangles ABC and CDA are congruent (ABC = CDA) by the HL theorem. This implies that the corresponding parts of the triangles are equal.
You provided the length AC = 84 m. In this situation, if AC is the hypotenuse for triangle ABC, then CA would also be the hypotenuse for triangle CDA since the triangles are congruent. However, to find the length of BA, we would need additional information, such as the lengths of the other legs (AB and BC) of triangles ABC and CDA.
If you have more specific details about the triangles or their dimensions, please provide that information, and I can assist you further in finding the length of BA.