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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