from a, b lies 24 km away on a bearing of 057 and c lies 15km away on a bearing of 347 find a)the distance between b and c. b)the

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1. Given : from a, b lies 24 km away on a bearing of 057° and c lies 15km away on a bearing of 347°

   To find : the distance between b and c

   Solution:

   Bearing is a direction measured from north and it tracks angle in clockwise direction with north line

   North represents zero degree,

   East is 90 degrees,

   South is 180 degrees

   West is 270 degrees.

   from a, b lies 24 km away on a bearing of 57°

   Hence location of b is 24cos57° along y axis ( North)

   and 24sin57° along x axis ( east)

   from a, c lies 15km away on a bearing of 347 °

   347° = – 13° and Cos (-13°) = Cos 13° and Sin (-13°) = -Sin(13°)

   Hence location of b is 15cos13° along y axis ( North)

   and 15sin13 along -x axis ( West)

   Distance between b and c

   = √(24cos57° – 15Cos13°)² + (24Sin57° -(-15Sin13°))²

   = √(24cos57° – 15Cos13°)² + (24Sin57° -(-15Sin13°))²

   = √2.3846 + 552.3609

   = √554.7455

   = 23.55

   the distance between b and c = 23. 55 km

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