Thread: The Law of Sines

I am having problems with the following questions. Could someone help me please.

2. Mackinac Island is located 35 miles N65 degrees 20 minutesW of Cheboygan, Michigan, where the Coast Guard cutter Mackinaw is stationed. A freighter in distress radios the Coast Guard cutter for help. It radios its position as N 25degrees 40 minutes W of Cheboygan. How far is the freighter from Cheboygan?

I would start by drawing a diagram. Start with a point where the pilot takes of from and then you know from the question that he lands 230km North of there. So draw a straight line up and label the length 230. Next we know that he flies at an angle of 85 degrees, so draw a line to the east or right from the starting dot at 85 degrees. Just short of a 90 degree line. Now on the way back he flew at 283 degrees, to find the angle just subtract 280 from 360 and you get 77. To find the last angle you just need to add 77+ 85 and then subtract that from 180 and you get 18 degrees.

So the 3 angles are 85, 77, and 18.

We use the law of sines:

a..........b..........c
----- = ----- = ------
SinA......SinB.....SinC

Angle A = 18
Angle B = 85
Angle C = 77

Side c = 230

So we get:

230
---- = 236.0499
Sin77


236.0499 = (a/Sin18)
Solve for a and you get a=72.94

236.0499 = (b/Sin85)
Solve for b and you get b=235.15

So the total length of the flight is 72.94 + 235.15 + 230 = 538.09