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.

Answered by Callum S. Maths tutor

18101 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Solve the following simultaneous equations: 3x - y = 1, 2x + 2y = 2


Find the centre and radius of the circle with equation: x^2 + y^2 -4x +8y = 5, and determine whether the point (7,-4) lies on the circle.


Emily bought 3 books and 2 apples, and she spent £19, while her brother, John, spent £15 on 1 book and 5 apples. What is the cost of one book and one apple?


Show that the recurring decimal 0.0151515..=1/66 (4H)


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo
Cookie Preferences