A person walks in the following pattern: 3.0 km north, then 2.1 km west, and finally 4.2 km south. (a) How far and (b) at what angle (measured counterclockwise from east) would a bird fly in a straight line from the same starting point to the same final point?

(a) 2.42 km

(b) 119.74°

Explanation:

(a)

The shortest distance from starting to end point is the hypotenuse

Where a is is base and b is height. Substituting 1.2 km for a and 2.1km for b then

(b)

The angle is given by the as indicated in the sketch

Towards East it will be 180-60.26=119.74°

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