The diagram shows the position of two ships, A and B, and a lighthouse L. Ship A is 5km from L on a bearing of 070° from L. Ship B is 3km from L on a bearing of 210° from L. Find the distance between A and B correct to 3.s.f.

(Draw diagram) From the diagram we can see that angle BLA= 210-70 = 140° . So for our triangle BLA we now have two sides and an included angle and we want to work out the length of the side opposite the angle. We need to use the cosine rule. (Relabelling sides) From the cosine rule we know that a²=b²+c²-2bccosA. Substituting for our values of b,c and A we get that a²=56.981, hence a=7.55km to 3 significant figures.