Question

For five days, several hikers walk the distance and direction described by the vector

⟨5, –2⟩ each day. The next day, they walk the distance and direction described by the vector ⟨–1, 8⟩. At the end of the six-day trip, what is their bearing from their starting location?

Answer 1

94.76°

Explanation:

Assuming the coordinates are <E, N>, the total distance from the start is ...

5<5, -2> +<-1, 8> = <5·5 -1, 5(-2) +8> = <24, -2>

These coordinates represent a vector south of east, so the bearing measured clockwise from north will be greater than 90°. The reference angle (with respect to a north-south line) will be ...

arctan(24/2) = 85.24°

The bearing is 180° -85.24° = 94.76°.