Answer:
see attached
possible 3rd side length: 12 or 13.93
Step-by-step explanation:
You want the possible lengths of the third side of a right triangle when two sides are known to be 5 and 13.
a) Long side is hypotenuse
The relation between the sides is ...
a² +b² = c²
If the two given sides are 'a' and 'c', then the third side is ...
b² = c² -a² = 13² -5² = 169 -25 = 144
b = √144 = 12
The third side is 12.
b) Long side is not hypotenuse
If the two given sides are 'a' and 'b', then the third side is ...
5² +13² = c²
c = √(169 +25) = √194 ≈ 13.93
The third side is √194, about 13.93.
