What Bearing Of A Third Object Will Provide The Best Fix?

If you take a bearing of 142° and 259° to two prominent objects on shore, what bearing of a third object will provide the best fix?

Solution:

Add the bearings of the two objects and then divide it by two.

(142° + 259°) ÷ 2 = 200.5° or 201° as rounded off. 

Third bearing

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Calculating Distance Off The Light When Abeam

While underway you sight a light 11° on your port bow at a distance of 12 miles. Assuming you make good course, what will be your distance off the light when abeam?

Given:
           Sin θ = 11°
      Distance = 12 nm

What is asked?

               Distance off abeam          

Solution:

In this problem you can figure out a plane triangle. 11° as your angle, 12 miles as your hypotenuse, and the distant off abeam as the opposite side.

So we can use the sine trigonometric function in solving this problem.

              Sin θ = opp

                          hyp

               Opp = hyp × Sin θ

Distant abeam = 12 × Sin 11°

                      = 12 × 0.190808

                      = 2.3 miles

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How To Calculate Time When Abeam Of The Light

You are steering 163°T and a light was picked up dead ahead at a distance of 11 miles at 0142. You change course to pass the light 2 miles off abeam to starboard. If you are making 13 knots, what will be the time when abeam of the light?

Given:

                   163°T = Course

                 0142H = Time during observation

      11 nm = Distance of the ligh at 0142H

        2 nm = Distance off abeam of the light

What is asked?

            Time when abeam of the light.

Solution:

            Step 1. We have to solve for the distance run to abeam by using Pythagorean theory.

                         Distance = √11² - 2²

                                      = √121 – 4

                                      = √117

                                      = 10.8 nm

Step 2. Divide the 10.8 nm by the speed to get the time interval.

                       TI = (10.8 nm ÷ 13 knots) x 60

                           = 49.84 or 50 mins

           

Step 3. Solving for time to abeam of the lighthouse. Add Time Interval to the time during observation.

            0142H

        +     50 min

               92 min

        +1hr-60 min

           0232H is the time when abeam of the light

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Bow And Beam Bearing Problem

A ship steaming on a course of 246° T at 17 knots. At 2107 a lighthouse was observed bearing 207 deg T and at 2119 the same lighthouse bears 179° T. What is the ship's distance off at second bearing?

SOLUTION:

Step 1. We have to get the angle at first and second observation. That is we to have subtract our course by   the observed bearings.

• 246° - 207° = 39° as our angle at first observation (<A)
• 246° - 179° = 67° as our angle at first observation (<B)

Step 2. We have to get the time interval by subtracting time at first and second observation.

• 2119H - 2107H = 12 mins

Step 3. Multiply the answer of step 2 by ship's speed & then divide by 60.

• (12 mins x 17 knots)  ÷ 60 = 3.4 miles

Step 4. Multiply the answer of step 3 by Sin <A.

• 3.4 x Sin 39° = 2.14

Step 5. Divide answer of step 4 by the difference of angle A and angle B

• 2.14  ÷ Sin 28° = 4.56 miles... is the ship's distance off at 2nd bearing.

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