An aeroplane flies from a town X on the bearing N45E to another town Y ,a distance of 200km it then changes course and flies to another town Z on a bearing of S60E,if Z is directly east of X, calculate to three significant figures.the distance from X to Z.The distance from Y to XZ

Question

An aeroplane flies from a town X on the bearing N45E to another town Y ,a distance of 200km it then changes course and flies to another town Z  on a bearing of S60E,if Z is directly east of X, calculate to three significant figures.the distance from X to Z.The distance from Y to XZ

oobleck · Accepted Answer

Draw triangle XYZ, and you can see that if you draw YK⊥XZ, you have handy angle XYK = 45° and angle ZYK = 30° So XZ = XK+KZ = 200/√2 + 200/√2 * √3 = 200/√2(1+√3) ≈ 386.37