Question

Bill has set his GPS to track his route. At the conclusion of his hike, the receiver indicates that he walked 3.5 miles north, 1.0 miles northeast, 1.5 miles south. How far away is Bill from his original position

Answer 1

$$\bold{d_1}=(0,3.5)$$

$$\bold{d_2}=(1.0 \cos(45),1.0 \sin(45))$$

$$\bold{d_3}=(0,-1.5)$$

$$\bold{d}=\bold{d_1+d_2+d_3}=(\cos(45),2+ \sin(45))$$

$$d=\sqrt{(\cos(45))^2+(2+\sin(45))^2}=2.8\ miles$$