The traveler went 5 km to the south and then another 12 km to the east. What is the modulus of the movement he accomplished.

Given:
S1 = 5 kilometers – module for moving the traveler to the south;
S2 = 12 kilometers – module for moving the traveler to the east.
It is required to find the modulus of displacement L (kilometers).
Since the south and east directions are mutually perpendicular to each other, then:
L ^ 2 = S1 ^ 2 + S2 ^ 2;
L = (S1 ^ 2 + S2 ^ 2) ^ 0.5 = (5 ^ 2 + 12 ^ 2) ^ 0.5 = (25 + 144) ^ 0.5 = 156 ^ 0.5 = 12.5 kilometers.
Answer: the travel module of the traveler is 12.5 kilometers.