The bearing of ships a and b from a port p arev225 and 116 respectively ship a is 3.91 from ship b on a bearing of 258 calculate the distance if ship a from p

2.55

Step-by-step explanation:

Draw a picture of the triangle formed by points P, A, and B.  The angle of the line from P to A is 225°.  The angle of the line from P to B is 116°.  The angle of the line from B to A is 258°, and the length of the line is 3.91.

The easiest way to solve this is by first finding the angle of the line from B to P.  Using interior angles, we can show that this is 180° − 116° = 64°.

Next, we can show that:

∠APB = 225° − 116° = 109°

∠ABP = 360° − (258° + 64°) = 38°

Finally, we can use law of sines to find AP.

AP / sin 38° = 3.91 / sin 109°

AP = 2.55

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