Double the Angle on the Bow
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Use this rule when the second bearing between the bow and the object is double the angle of the first. For example, if the first bearing is 22 and the second is 44, you can use this rule.
 
What it tells you is that the distance run between the two bearings will be equal to the distance from the second observation point to the object.
 
This works because, as you can see in the figure at right, the triangle created when drawn out is isoceles, meaning that two of the sides and two of the interior angles are the same. In a triangle, the sum of the three interior angles will be 180. If one angle is a, another is 180-2a, and the last is b, simply solving the equation
180 = a + b + 180 - 2a will show that a = b, and therefore both angles are the same. Because both angles are the same, the sides opposite them will be of equal length.

Back to Special Case Bearings

double_angle.jpg

Example:
Question: You are steering course 090 at 18 kts. At 0800, you spot a spar buoy at 068. At 0820, the same buoy bears 046. How far away is the buoy at the time of the second observation.
 
Solution:
-First, find your relative bearings
     090 - 068 = 22
     090 - 046 = 44
-Knowing that your second angle is twice the first, you can assume that the distance to the object is equal to the distance run.
-Find the distance run.
     0820 - 0800 = 20 min
     20min/60 x 18 = 6nm
-DR equals dist to object, 6nm.