Hi-

Suppose that the boat has sailedA boat sailing from A to B travels in a straight line until the captain realises he is off course. The boat is turned through an angle of 60 degrees, and then travels another 10 km to B. The trip would have been 4 km shorter if the boat had gone straight from A to B. How far did the boat travel?xkm to a point C before the captain changes course. So you can draw a triangle ABC with the following information:

- AC =
xkm- CB = 10 km
- Angle ACB = 180 - 60 = 120 degrees
- AB is 4 km less than (
x+ 10). So?

You can now use theCosine Ruleon this triangle:

Now remove brackets and simplify. (Be careful with the cosine of 120 degrees - it'snegative.) If you do it right, it turns out to be a very easy equation forx.

If yours doesn't work out to be easy, let me know, and I'll give you a bit more help.

Grandad