Answer:
4.19 km and 107.35 degrees north of east
Explanation:
So in the end, the truck is (2.6 + 1.4 = 4km) north and 1.25 km west from the warehouse. We can use the Pythagorean formula to calculate the magnitude and direction α of the truck displacement from the warehouse:
[tex]s = \sqrt{s_n^2 + s_w^2} = \sqrt{4^2 + 1.25^2} = \sqrt{16 + 1.5625} = \sqrt{17.5625} = 4.19[/tex]
km
[tex]tan\alpha = \frac{s_n}{s_w} = \frac{4}{1.25} = 3.2[/tex]
[tex]\alpha = tan^{-1}3.2 = 1.27 rad \approx 72.65 degrees [/tex] north or west or (180 - 72.65) = 107.35 degrees north of east
