Answer:
[tex]20\:\mathrm{miles}[/tex]
Step-by-step explanation:
After travelling two hours, the two cruise ships form a triangle. One of the legs of this triangle will be the distance Cruise A travelled, and another will be the distance Cruise B travelled. We can find the distance they travel using:
[tex]s=\frac{d}{t}, d=s\cdot t[/tex]
Cruise A is travelling at 18 miles per hour for 2 hours. Therefore, Cruise A has travelled:
[tex]d=s\cdot t=18\cdot 2=36\:\mathrm{miles}[/tex]
Cruise B is travelling at 15 miles per hour for 2 hours. Therefore, Cruise B has travelled:
[tex]d=s\cdot t=15\cdot 2=30\:\mathrm{miles}[/tex]
Because we are given the angle between these legs, we can use the Law of Cosines to find the third leg. The Law of Cosines is given by:
[tex]c^2=a^2+b^2-2ab\cos C[/tex], where [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex] are interchangeable. Let [tex]c[/tex] represent the distance between the two cruises. We have:
[tex]c^2=36^2+30^2-2\cdot36\cdot30\cdot \cos 35^{\circ},\\c^2=426.63,\\c\approx \fbox{$20\:\mathrm{miles}$}[/tex](one significant figure).
9514 1404 393
Answer:
20.7 miles
Step-by-step explanation:
The distance that A travels in the same direction as B is ...
(18 mi/h)(2 h)cos(35°) = 29.489 mi
So, the difference in distances in that direction is ...
(15 mi/h)(2 h) -29.489 mi = 0.511 mi
__
The distance A travels in the direction perpendicular to B is ...
(18 mi/h)(2 h)sin(35°) = 20.649 mi
So, the straight-line distance between the ships is the hypotenuse of the right triangle with these distances as legs:
AB = √(0.511² +20.649²) = √426.632 . . . miles
AB = 20.655 miles ≈ 20.7 miles . . . separation after 2 hours
