An aeroplane flies from a town X on a bearing of N45 degree E to another town Y ,a distance of 200 cm it then changes course and flies to another town Z on a bearing of S60 degree E .if Z is directly tast of X .calculate ,correct to 3significant from X to Z

Answer 1

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An aeroplane flies from town X on a bearing of N45'E to another town Y, a distance of 200km. It then changes course and flies to another town Z on a bearing of S60'E. If Z is directly east of X, calculate to 3sf, the distance from X to Z and the distance from Y to XZ.

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Answer 2

Draw triangle XYZ,
Law of sine: XY/sin45 = YZ/sin30,
200/sin45 = YZ/sin30,
200 = YZ*sin45/sin30,
YZ = 141.4 km.

200/sin45 = XZ/sinY,
200/sin45 = XZ/sin105,
XZ = ?.