Consider a right triangle that has these dimensions: the side opposite angle a is 6 meters and the side adjacent angle a is 8 meters. how long is the hypotenuse?

To determine the length of the hypotenuse, we need a relation that would relate the other legs and the hypotenuse of the triangle. So, we would need to use the Pythagorean theorem which is an equation that relates the hypotenuse with the other legs of a right triangle. It is to be noted that this is only usable for right triangles only. It is expressed as follows:

c^2 = a^2 + b^2

where c is the hypotenuse and a, b are the other legs.

c = √(a^2 + b^2)
c = √(6^2 + 8^2)
c = √100
c = 10 m

Therefore, the length of the hypotenuse with the other legs having a length of 6 and 8 would be 10 m.