A surveyor standing at a point X sights a pole Y due east of him and a tower Z of a building on a bearing of 046°. After walking to a point W, a distance of...

A surveyor standing at a point X sights a pole Y due east of him and a tower Z of a building on a bearing of 046°. After walking to a point W, a distance of 180m in the South- East direction, he observes the bearing of Z and Y to be 337° and 050° respectively.

(a) Calculate, correct to the nearest metre : (i) |XY| ; (ii) |ZW| 

(b) If N is on XY such that XZ = ZN, find the bearing of Z from N.