🔍 Key Concepts

• Relative bearings and abeam – what does it mean when an object is "abeam" of your vessel? • Using your ship’s course and two observed bearings to determine the change in relative bearing over time. • Using speed and time run between bearings to find the distance traveled, then relating that to distance off at abeam using a right triangle or the sin rule.

💭 Think About

• First convert each true bearing of the light to a relative bearing from your ship’s head (263°T). How many degrees has the light moved relative to your bow between the two sights? • From the time difference and your speed, find how far you traveled between the two bearings. How can this run between bearings form one side of a triangle whose other side is the distance off at abeam? • At the instant the light becomes abeam, what is the relative bearing? How does that help you set up the geometry to solve for distance off using the angle changes you observed?

✅ Before You Answer

• Be sure you are using relative bearings (from the ship’s head) when talking about “abeam,” not true bearings. • Check that your time interval (in minutes) is correctly converted to hours before multiplying by speed in knots: ( \text{Distance} = \text{Speed} \times \text{Time (hours)} ). • Verify that the triangle you construct uses the correct included angle between the two lines of position based on the change in relative bearing, and that the side you solve for corresponds to the distance off at abeam, not the distance run.