Question 1137158
Ship A, sailing due east at 8 km/h, sights ship B 5 km to the southeast when ship B is sailing due north at 6 km/h.
 How close to each other will the two ships be when they pass? 
:
The relationship of the two ships is such that their paths will form a right triangle with equal sides.
:
let t = time when ship A will be exactly due north of B, this is the their closest point
For the moment let's assume they are going the same speed, 8 km/h
Solving the right triangle
(8t)^2 + (8t^2) = 5^2
64t^2 + 64t^2 = 25
128t^2 = 25
t = {{{sqrt(25/128)}}}
t = .442 hrs is the time when ship A will exactly north of ship B
distance traveled .442 * 8 = 3.5355 km
During this time ship B will travel .442 * 6 = 2.652 km
therefore
3.355 - 2.652 = .8835 km will be the distance between them, the minimum