Answer:
Point A is [tex]\sqrt{41}[/tex] miles far from point B.
Step-by-step explanation:
Draw a diagram by using the given information.
1. Move 8 units up to reach at point Q. (Walk from point A ,8 miles due north).
2. Move 5 units right to reach at point R. (5 miles dues east)
3. Move 4 units down to reach at point B. (4 miles due north to point B)
4. Drawn a line PB as shown below.
From the below figure it is clear that
AP = 8-4 = 4 miles
PB = QR = 5 miles
Using Pythagoras we get
[tex]hypotenuse^2=perpendicular^2+base^2[/tex]
[tex]AB^2=AP^2+PB^2[/tex]
[tex]AB^2=4^2+5^2[/tex]
[tex]AB^2=41[/tex]
Taking square root on both sides.
[tex]AB=\sqrt{41}[/tex]
Therefore, point A is [tex]\sqrt{41}[/tex] miles far from point B.
