Cosine Rule

I cant do this question, i think im drawing the diagram wrong, thanks if anyone can help (Diagram attatched)

A man walks 5km due north and then a further 4km on a bearing of 120degrees

a) Draw a clear sketch of this journey, stating all known lengths and angles.
b) How far is he from where he started(to 3 significant figures)?

a) see diagram, can you check if its correct?

b) b^2 = a^2+c^2 - [2 x a x c x CosB]

b^2 = 4^2 + 5^2 - [2 x 4 x 5 x Cos120]

= 16 + 25 - [-20]

= 61

Therfore b = sqroort(61) = 7.810249676km = 7.81km(3sf)

I cant get the back of the book answer which is 4.58km, i think ive drawn the diagram incorrectly. Any help would be greatly apprectiated! :smile:

cosinerule.JPG6.5KB

Reply 1

Talya

Diagram = Incorrect

The angle ABC on your diag should be 60 degrees. The angle between the North and the outside of the triangle in 120 degrees. Bearings are always measured from the North.

I can't draw in paint but try again and post that, and we'll see.

Reply 2

dec0!

Ok thanks a lot i did the same thing but this time used the angle as 60 degrees
and i got the correct answer, check my diagram to check if it is correct ?