ZJSG09112007
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The bearings of ships A and B from a port P are 225° and 116° respectively. Ship A is 3.9km from ship B on a bearing of 258°.
Calculate the distance of ship A from P.

Please show workings and diagrams.​

Respuesta :

mhanifa

Answer:

  • 2.54 km

Step-by-step explanation:

See the attached

All given details are reflected in the diagram (not to scale)

  • PA is at 225°, PB is at 116°, BA is at 258°
  • AB = 3.9 km
  • AP = x
  • m∠P = 225° - 116° = 109°
  • m∠A = 258° - 225° = 33°
  • m∠B = 180° - (109° + 33°) = 38°

Use the law of sines:

  • x/ sin 38° = 3.9 / sin 109°
  • x = 3.9 sin 38° / sin 109°
  • x = 2.54 km (rounded)
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