1.(a) A man walks due west for 4km. He then changes direction and walks on a bearing of 197° until he is south-west of his starting point. How far is he then from his starting point?(b)The bearing of a house from a point A is 319°. From a point B, 317m due east of A the bearing of the house is 288°.How far is the house from A?(c) An aeroplane flies from a 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 (i)the distance from X to Z (ii) the distance from Y to XZ(d) from points A and B on level ground, the angle of elevation of the top of a building are 25° and 37° respectively. If |AB|=57m, calculate the distances of the top of the building from A and B if they are both on the same side of the building.

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Answers
(a)8.15km
(b)190m
(c)i) 386km (ii) 141km
(d) 165m; 116m