Mathematics, 17.01.2021 01:10 strikeboystorm

Two cruise ships leave the same port with a 35° angle between their path. Cruise A is traveling at 18 miles per hour and Cruise B is traveling at 15 miles per hour. If they travel in a straight path, find the distance between the cruise ships after 2 hours

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Answer from: lashondrascott

$20\:\mathrm{miles}$

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:

$s=\frac{d}{t}, d=s\cdot t$

Cruise A is travelling at 18 miles per hour for 2 hours. Therefore, Cruise A has travelled:

$d=s\cdot t=18\cdot 2=36\:\mathrm{miles}$

Cruise B is travelling at 15 miles per hour for 2 hours. Therefore, Cruise B has travelled:

$d=s\cdot t=15\cdot 2=30\:\mathrm{miles}$

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:

$c^2=a^2+b^2-2ab\cos C$ , where , , and are interchangeable. Let represent the distance between the two cruises. We have:

$c^2=36^2+30^2-2\cdot36\cdot30\cdot \cos 35^{\circ},\\c^2=426.63,\\c\approx \fbox{$20\:\mathrm{miles}$}$ (one significant figure).

Answer from: JuniperGalaxy

9514 1404 393

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

Answer from: Quest

describing distributions is one of the key skills you’ll need to earn a high score on the ap statistics exam. if you need proof of this, just flip through some past exam questions, which can be found at the collegeboard website. you’ll notice that the first free response question is almost always a question requiring you to look at a graph and describe it.

step-by-step explanation: just trying to get points sorry : (

Answer from: Quest

no solution

step-by-step explanation:

there is not enough information in the problem to solve.

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Two cruise ships leave the same port with a 35° angle between their path. Cruise A is traveling at 1...