# Application of the Sine Rule

• Sep 29th 2010, 01:57 AM
BinaryBoy
Application of the Sine Rule
Hi everyone,

As I was teaching myself the Sine Rule, I happened upon the following question, which needless to say has stumped my attempts to solve it thus far:

Here it is:

From a fire tower, A, a fire is spotted on a bearing of N42 degrees E. From a second tower, B, the fire is on a bearing of N12 degrees W. The two fire towers are 23 kilometres apart and A is N63 degrees W of B.

I assume that N 42 degrees E means that the fire is 42 degrees away due East. And N 12 degrees West means that it is 348 degrees True. But I am not in any way confident on that.

Any help solving this problem will be highly appreciated!

Thanks,

Nathaniel
• Sep 29th 2010, 02:14 AM
Educated
• Sep 29th 2010, 02:21 AM
pickslides
Have you drawn a picture? What is the actual question? i.e, what is the angle/distance from X to Y...?
• Sep 29th 2010, 02:46 AM
BinaryBoy
Sure. I'll attach the one I drew now, and show the calculations I have performed to the present.

Attachment 19121)

I do not think it is correct. (And it certainly isn't artistic!)

Calculations for Tower B:

a / sin A = b / Sin B

x / sin 48 = 23 / sin 81

x = (23 / sin 81) x sin 48

x = 17.30

x should have yielded 27.46

(Above is my latest variation. I've tried others, but to no avail).

Thanks,

Nathaniel
• Sep 29th 2010, 03:07 AM
Educated
This is very confusing. Bearings always start at north and go clockwise... but in this question, they put make the bearing go counterclockwise.

Here's my interpretation of it:

http://www.mathhelpforum.com/math-he...-bearing-1.png
Attachment 19122

Now I don't know where to place the third angle, the third piece of information states: "A is N63 degrees W of B"

But A isn't west of B, it is to the east of B.

I'm not getting your picture either BinaryBoy. I thought that the fires were more north than the tower?