Why 79 degrees instead of 101 degrees?

[LBOlson]

Two ocean liners leave from the same port in Puerto Rico at 10:00 a.m. One travels at a bearing of N 46 degrees W at 12 miles per hour, and the other travels at a bearing of S 55 degrees W at 14 miles per hour. Approximate the distance between them at noon the same day. This is the problem.

When I solved this problem I used the law of cosines and used cos 101 degrees but I guess I was suppose to use cos 79 degrees. I don't understand why. Can you explain it to me?

 

[stapel]

Two ocean liners leave from the same port in Puerto Rico at 10:00 a.m. One travels at a bearing of N 46 degrees W at 12 miles per hour, and the other travels at a bearing of S 55 degrees W at 14 miles per hour.

"North forty-six degrees from west", which is how I'm interpreting "N 46 degrees W", means that you go to the negative x-axis (that is, to the "westerly" arm of your graph) and rotate clockwise forty-six degrees. (here) The other direction is fifty-five degrees counter-clockwise from the same axis. The angle between them, then, is 101 degrees.

Approximate the distance between them at noon the same day. This is the problem.

When I solved this problem I used the law of cosines and used cos 101 degrees but I guess I was suppose to use cos 79 degrees. I don't understand why. Can you explain it to me?

In order to explain what you've seen, you'll need to provide us with that information. I would note, however, that 101 is 90 + 11, while 79 = 90 - 11. Perhaps some mirroring (and sign-changing) happened somewhere in the steps you're viewing...?

 

[skeeter]

"North forty-six degrees from west", which is how I'm interpreting "N 46 degrees W", means that you go to the negative x-axis (that is, to the "westerly" arm of your graph) and rotate clockwise forty-six degrees.

North 46 degrees West is interpreted as starting the ray due North (+ y-axis), then turning the ray 46 degrees toward the West.

Whoever came up with this "textbook" method for designating directions should be flogged. Using the real world method ... due North as 000 degrees, East as 090, South as 180, and West as 270 removes the ambiguity for designating directions.

 

[Ishuda]

Two ocean liners leave from the same port in Puerto Rico at 10:00 a.m. One travels at a bearing of N 46 degrees W at 12 miles per hour, and the other travels at a bearing of S 55 degrees W at 14 miles per hour. Approximate the distance between them at noon the same day. This is the problem.

When I solved this problem I used the law of cosines and used cos 101 degrees but I guess I was suppose to use cos 79 degrees. I don't understand why. Can you explain it to me?

Well, if you do as skeeter indicates, you get 79 degrees as the proper angle to use.

 

[stapel]

North 46 degrees West is interpreted as starting the ray due North (+ y-axis), then turning the ray 46 degrees toward the West.

I stand corrected. Most resources that pop up seem to be math textbooks and the like, but they're wrong. :shock:

The quote above gives the right way to interpret the lingo, at least in real life. (here). Of course, if you're working out of a textbook (one of the many) that uses the wrong way, then "the right answer" will be the one that relies on that wrong definition.

Apparently, that is not the case here. So, Original Poster, please do use the correction posted by the other helpers.