Finding Ship's Distance Off The Second Bearing And When Abeam

A ship on course of 253° T at 14 knots. At 2329 a lighthouse was observed bearing 282° T. At 2345 the same lighthouse bears 300° T. Find the ship’s distance off the second bearing and when abeam?


Given:

              Course = 253°
               Speed = 14 knots
     First Bearing = 282°
 Second Bearing = 300°

Find:
             A.) Ship’s distance off the second bearing
             B.) Ship’s distance when abeam

Solution:

1. Find first Angles  A, B, C:

       a.)Co = 253° T
        Brg1 = 282° T 
    Angle A = 29° R

      b.) Co = 253° T
         Brg2 = 300° T
     Angle B = 47° R

     c.) Angle B = 47° R
          Angle A = 29° R
          Angle C = 18° R 

2. Then solve for AB (Distance Run Between 1st & 2nd Observation)

               AB = ( Time 2 – Time 1 ) x Speed
                     = ( 2345 – 2329 ) x 14 knots
                     = 16 minutes x 14 knots
                AB = 3.73 nautical miles

 3. Solve for Distance off at second bearing (BC): (By SINE Law)

                BC = Sin A x AB 
                              Sin C
                 BC = Sin 29° x 3.73
                              Sin 18°
                 BC = 5.9 nautical miles (Distance off at 2nd bearing)

4. Solve for Distance at Abeam (CD) : (By SOH – CAH – TOA)

                CD = BC x Sin B
                CD = 5.9 x Sin 47°
                CD = 4.3 nautical miles ( Distance at Abeam)

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