Question

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°.

Answer 1

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)