🔍 Key Concepts

• Difference between true wind, apparent wind, and vessel speed as velocity vectors • How to set up a velocity triangle (vector diagram) using the ship’s course, apparent wind, and true wind • Using the law of cosines when you know two sides and the included angle between them

💭 Think About

• Sketch the ship’s course as one vector and the apparent wind as another, with the 40° angle between them. Which side of the triangle represents the true wind? • Given two known sides (17 knots and 15 knots) and the angle between them (40°), which trigonometric relationship lets you solve for the third side? • Before doing exact math, estimate: should the true wind speed be closer to 15 knots, closer to 17 knots, or quite different, given the small 40° angle between them?

✅ Before You Answer

• Be clear which vectors you are adding: ship’s velocity through the water and true wind give the apparent wind relative to the ship • Confirm that the angle you plug into your formula is the actual angle between the ship’s course and the apparent wind direction (40° off the bow) • After computing, check whether your result is reasonable: it must be between the difference and the sum of 15 and 17 knots (between 2 and 32), and also make sense relative to the small 40° angle