Ok, so this is simpler than I first thought. This is way I should have done it the first time.
First of all, this is the situation. The distance the friend’s boat will travel is 5t (t = hours) NM on a course of 036 Deg T. You are 84NM from him at a bearing of 096 Deg T relative to his boat. In order to meet, you will travel a distance of 7t NM at some unknown heading.
It’s obvious that the angle between the track of your friend’s boat and the bearing from his boat to yours is 96 – 36 = 60 Deg
Remember the law of sines? It’s handy. It says that for any triange the ratios of the length of each side to the angle opposite that side are equal.
If A is the angle between the heading you need and the bearing from your boat to your friends,
that means: sin60 / 7t = sinA / 5t
or sin –1 (5/7 * sin 60) = A
A = 38.2 Deg
Your heading then should be 96 + 38.2 + 180 = 314.2 Deg T
How long to get there?
We all remember that the sum of all the internal angles of a triangle = 180 so the remaining angle is 180 – 38.2 – 60 = 81.8 Deg
From the law of sines, 7t = 84 * sin 60 / sin 81.8
t =10.5 hours
There are 10 kinds of people. Those who understand binary and those who don't.
Last edited by CapnHand; 02-22-2007 at 10:22 PM.