Trigonometry questions(trig function applications)

[ConfusedMath]

I am stumped on this word problem,
"Two sailboats leave a harbor in the bahamas at the same time. The first sails at 23 mph in a direction 330 degrees. The second sails at 34 mph in a direction 190 degrees. Assuming both maintain speed and heading, after 2 hours how far apart are the boats?"

I found the distance of each boat( 23 mph*2, 34 mph*2) and set up 46=a and 68=b
This is a recreation of the pic I drew, though I'm sure the angles arenot to scale.
(please excuse how crappy it is )

If I knew what angle C was I could find the distance(little c) with the law of cosines,but
I don't know how to find the angle since the two angles (190 and 330) do not add up to 180.(ignore the straight line I have there, my angles are not drawn well to proportion)
I only have two sides,and as far as I'm told with the info it is not a right triangle so can't use pythagorean. How do I find the side,or other angles when I only have 2 sides,no supplementary angles and not a right triangle?


I also wanted to know if I went about this problem correctly,
"Two points A & B are on opposite sides of a building. A man selects a third point C to place a flag. Place C is 53 ft from A and 67 ft from B. The angel ACB is 49degrees. How far apart are A and B?"
I drew a picture and used the law of cosine,
a=67 b=53 Cangle=49degrees
c^2=a^2+b^2-2abCosC
c^2=67^2+53^2-2(67)(53)Cos49degrees
7298-7102cos49
196cos49
c^2=128.59
c=sqrt(128.59=
11.34

 

[wjm11]

I am stumped on this word problem,
"Two sailboats leave a harbor in the bahamas at the same time. The first sails at 23 mph in a direction 330 degrees. The second sails at 34 mph in a direction 190 degrees. Assuming both maintain speed and heading, after 2 hours how far apart are the boats?"

I found the distance of each boat( 23 mph*2, 34 mph*2) and set up 46=a and 68=b
This is a recreation of the pic I drew, though I'm sure the angles are not to scale.
(please excuse how crappy it is )

If I knew what angle C was I could find the distance(little c) with the law of cosines, but
I don't know how to find the angle since the two angles (190 and 330) do not add up to 180.(ignore the straight line I have there, my angles are not drawn well to proportion)
I only have two sides, and as far as I'm told with the info it is not a right triangle so can't use Pythagorean. How do I find the side, or other angles when I only have 2 sides, no supplementary angles and not a right triangle?

Your picture did not come through for me to see, so I am not sure if you are measuring your angles from north (as headings) or from the x-axis. No matter. I will assume you drew them starting from the x-axis. Here is how to figure out your angle:

The boat that went 46 miles in direction 330 degrees lies in the 4th quadrant. The boat that went 68 miles in direction 190 degrees lies in the 3rd quadrant. The angle between them is simply 330 – 190. If you draw the angles on your sketch, this should become obvious. Hope that helps.