Answer: The distance between them is 8.38 km
Explanation:
Let's suppose both of them start at the point (0km, 0km), and that Jack walks along the positive x-axis, then Jill walks at an angle of 105° measured from the positive x-axis.
After 45 minutes, jack has walked 4.5km, then if his initial position was (0 km, 0 km)
Then his new position will be (4.5km, 0km)
Jill has walked 6km, but we need to write this in rectangular components.
We can think in this as a triangle rectangle, then the components will be:
x-component = 6 km*cos(105°) = -1.55 km
y-component = 6km*sin(105°) = 5.80 km
Then the new position of Jill is ( -1.55km, 5.80km)
Now, we know that the distance between two points (a, b) and (c, d) is:
Distance = √( (a - c)^2 + (b - d)^2)
Then the distance between Jill and Jack will be equal to the distance between ( -1.55km, 5.80km) and (4.5km, 0km)
This is:
Distance = √( (-1.55km - 4.5km)^2 + (5.80km - 0km)^2)
Distance = 8.38 km
This means that they are 8.38km apart.