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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 traveli
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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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Mathematics
3 years
2021-08-22T04:08:03+00:00
2021-08-22T04:08:03+00:00 2 Answers
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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
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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:
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:
Cruise A is travelling at 18 miles per hour for 2 hours. Therefore, Cruise A has travelled:
Cruise B is travelling at 15 miles per hour for 2 hours. Therefore, Cruise B has travelled:
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:
, where , , and are interchangeable. Let represent the distance between the two cruises. We have:
(one significant figure).