Suppose that the boat has sailed x km to a point C before the captain changes course. So you can draw a triangle ABC with the following information:A 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?
- AC = x km
- CB = 10 km
- Angle ACB = 180 - 60 = 120 degrees
- AB is 4 km less than (x + 10). So?
You can now use the Cosine Rule on this triangle:
Now remove brackets and simplify. (Be careful with the cosine of 120 degrees - it's negative.) If you do it right, it turns out to be a very easy equation for x.
If yours doesn't work out to be easy, let me know, and I'll give you a bit more help.