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anonymous
 5 years ago
if a two ships left the same port at the same time but ship A left at N35'E45 degrees at a speed of 25 mph and ship B left at N24'56degrees at a speed of 25 mph, how far apart would they be in 4 hours?
i dont understand what formula to use law of sines? law of cosines? help!!
anonymous
 5 years ago
if a two ships left the same port at the same time but ship A left at N35'E45 degrees at a speed of 25 mph and ship B left at N24'56degrees at a speed of 25 mph, how far apart would they be in 4 hours? i dont understand what formula to use law of sines? law of cosines? help!!

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Hi, this site keeps crashing on me. Use cosine rule  the ships will have an angle between them equal to the difference of their angles, and they will have traveled 100miles in 4 hours, so you have your side lengths. The distance is the distance between them .

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the second one is actually S24'E56 so so do i find the hypotenuse?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0If you can wait, I can send you a solution later. I can't do anything on the machine I'm on right now.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes i can wait! and ship b is 23 mph sorry for all of the mistakes

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Okay, this is going to be an application of the cosine rule. Do you know how to get angles when they're given in this form first?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes, you put them in the calculator using 2nd angle

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yeah, but I mean geometrically. I'm drawing a picture of the situation.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Now, the angle (when you're given it in this form, i.e. North blah blah) is swept out from the north pole towards where the object is. Here, ship B has the smaller angle (blue) and ship A has the larger. What you're being asked to find is the distance between the ships at the end of 4 hours.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0The distance is the line in pink. Now, since speed is *defined* as \[(speed)=\frac{(distance)}{(time)}\]it means,\[(distance)=(speed) \times (time)\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh, but wouldnt ship b be in the 4th quadrant since its angle is SE?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh ok, so then you would get 100 mi and 92 mi which give you the side lengths?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0The distance ship A travels in 4 hours is then,\[d_A=25\frac{mi}{h}\times 4 h=100 miles\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Ship B will, in 4 hours, travel,\[d_B=23\frac{mi}{h} \times 4 h = 92 miles\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Now you have the two distances  the blue and red lines.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0All you need to do is now find the angle BETWEEN the two ships  this will stay the same since they don't change course. The angle between them is the angle in pink. It's given by the difference between the larger and smaller angles.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\theta = 35^o45' 24^o56'=10^o49'\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok that makes sense, but what if the angle was supposed to be in the 4th quadrant since i wrote it wrong

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I'm not sure what you mean.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0since ship b was S24E56 but i wrote it as N24E56

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0like ship b was supposed to be S24E56 not N24E56

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0To say S24E56 means "24 degrees, 56 minutes from magnetic South in the Easterly direction." So you move from the 'South' line and sweep upwards towards the East by 24 degrees, 56 minutes.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0The first letter tellls you what pole to start from, then the second letter tells you whether to sweep left or right (left = West, right = East).

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0The problem is set up in the same way  you're still going to have to use the cosine rule because you need to find the distance opposite an angle, where that angle is BETWEEN two sides you know the value of.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so when im finding the angle, do i have to include the 56 minutes part when using the law of cosine?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Is this what you've got?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Now we have to find the angle IN BETWEEN from the info. we're given.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so to do this, do i subtract the two give angles from 180?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Note, from your picture, that the red angle and the green angle will sum to 90 degrees. The blue angle and purple angle will sum to 90 degrees also.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0We need (green) + (purple), since this is the angle in between. We have, (red) + (green) + (purple) + (blue) = 90 + 90 = 180 degrees. We know that (red) = 35degrees, 45 minutes and that (blue) = 24 degrees, 56 minutes, so

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0(green) + (purple) = 180  35deg.45min  24deg.56min. = 119deg.19min.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0This is your angle in between the two lines. We have the distances calculated above, so we have the following now:

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0(They're both the same). Okay, so now we can use the cosine formula: \[a^2=100^2+92^22(100)(92)\cos(119^o19')\]to get\[a^2 \approx 27473\]which means that the distance is (after taking the square root),\[a \approx 165.75\]miles.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0thank you. i totally understand it now!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Good :) Good luck with it. If you need anymore help, come back to the site  I might be around.
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