# Thread: Application of the Sine Rule

1. ## 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

2. Have you tried drawing a diagram to help you visualise it?

3. Have you drawn a picture? What is the actual question? i.e, what is the angle/distance from X to Y...?

4. Sure. I'll attach the one I drew now, and show the calculations I have performed to the present.

)

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

5. 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:

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?