# Law of sines

1. Jan 23, 2010

### morr485

1. Two towers A and B are 18.5 miles apart. The bearing from A to B is N65E. A fire is spotted
by ranger at both towers. Its bearing from A and B are N28e and N16.5W. This makes a
triangle with A and B and C the fire.
Can anyone give me a clue and finding angles A and B?

2. a/sin A = b/sin B

3. I found angle B was 138.5, except it wasn't right.

Last edited: Jan 24, 2010
2. Jan 23, 2010

### morr485

I'm trying to post my question.

3. Jan 24, 2010

### HallsofIvy

Staff Emeritus

Mark a point "A" on your paper. Draw a vertical line (representing north) and a horizontal line (representing east/west). Draw a line slanting 65 degrees to the right of the upward vertical (N65E)and mark its end "B". Draw a line from A slanting 28 degrees to the right of the upward vertical (N28E) and draw a line from B slanting 16.5 degrees to the left of the upward vertical (N16,5W). The fire is at the point where the two lines meet and it and A and B form the triangle you want.

Now you should be able to see that the angle at A is the difference 65- 28= 37 degrees inside the triangle. At B, the lilne from A makes an angle of 65 degrees with the vertical (opposite interior angles with parallel lines) and that, the 16.5 degree angle, and the angle inside the triangle make make a straight,vertical, line. Their sum must be 180 degrees so the angle inside the triangle, at B, is 180- 65- 16.5 degrees.