Answer:
55.96 miles
Step-by-step explanation:
Distance = Speed X time
Car first moved east for 1 hr , distance = 40 x 1 = 40 miles
Car then moved north-east for 30 min, distance = 40 x 0.5 = 20 miles
From trigonometry,
sin 45 = [tex]\frac{y}{20}[/tex] ; y = 20 sin 45 ; y= 14.14 miles
cos 45 = [tex]\frac{x}{20}[/tex] ; x = 20 cos 45 ; x = 14.14 miles
using Pythagoras theorem;
[tex]z^{2}[/tex] = [tex]y^{2}[/tex] + [tex](40+x)^{2}[/tex]
= [tex]14.14^{2}[/tex] + [tex](40+14.14)^{2}[/tex]
= 3131.08
[tex]z^{2}[/tex] = [tex]\sqrt{3131.08}[/tex]
z = 55.96 miles
