**A ship sails on a bearing of 045o for 299km then changes direction and sails on a bearing of 135o for 408km. Finally it then turns and sails for 188km on a bearing of 225o. How far is it now in a straight line from its starting position. Give your answer to the nearest kilometre.**

**Answer:**

I hope I can draw the route line, but I don’t think Latex editor supports uploading a photo. If you draw it correctly, the route line will make an irregular shaped diamond. The angle must be drawn from horizontal base, similar to trigonometry quadratic angles.

Suppose the first trip (45 degrees) is from A to B (toward northeast)

Suppose the second trip (135 degrees) is from B to C (toward northwest)

Suppose the third trip (225 degrees) is from C to D (toward southwest)

The straight line from its starting position would be A to D

The triangle ABC and ACD will be right triangles

Here’s the mathematical calculation:

By using pythagoras law:\

Review triangle ABC