Answer:
about 11.4 km
Explanation:
The law of cosines can be used to find the third side of a triangle when two sides and the angle between them are known.
Law of Cosines
The law of cosines tells us ...
c² = a² +b² -2ab·cos(C)
In the triangle modelling the problem geometry, the angle between the walking directions is 120°, so the distance from start can be found from ...
c² = 8² +5² -2·8·5·cos(120°) = 129
c = √129 ≈ 11.358
The distance is about 11.4 km from the starting point.