Bearings & Navigation Worksheet/Game

Bearings & Navigation Worksheet/Game
Welcome to Bearings & Navigation Worksheet/Game. In this game, you’ll need to apply your knowledge of Angles of Elevation and Depression to find the heights of objects or the distances between objects. Scroll down the page for a more detailed explanation.

 

 

1. The Mission
   You must complete a voyage consisting of 10 navigational legs. In each leg, you are given a bearing (the direction) and a distance. Your job is to calculate the specific “Easting” (how far East/West) or “Northing” (how far North/South) the vessel has traveled.
   

2. Mastering Three-Figure Bearings
   In this game, bearings are measured differently than in standard math geometry:
   Measured from North: 000° is always straight up.
   Clockwise only: You always count degrees turning to the right.
   The “Zero” Rule: Bearings under 100 are written with a leading zero (e.g., 045°).
   

3. The Captain’s Trig (Nautical SOH-CAH-TOA)
   Because bearings start from the vertical North line instead of the horizontal x-axis, the standard sin and cos roles are swapped:
   To find North/South (Northing): Use Cosine.
   Distance · cos(bearing)
   To find East/West (Easting): Use Sine.
   Distance · sin(bearing)
   To find the Bearing (θ): Use Inverse Tangent.
   \(\tan(\theta) = \frac{East}{North}\)
   

4. Game Controls
   Plot Your Course: Select one of the four buttons that matches your calculation.
   Navigation Feedback:
   Steady as she goes! (Gold): Your calculation was perfect.
   Off Course! (Red): You made a navigational error. The correct bearing or distance will be highlighted.
   Chart Course (Show Steps): If you hit a reef (get an answer wrong), click this button to see the math used to find the correct path.
   Abort Voyage: Use the link at the bottom to return to the main menu and restart your training.
   

5. Essential Navigator Tips
   Due North/South/East/West: If a bearing is 000°, 090°, 180°, or 270°, you don’t need a calculator! One component will be the full distance, and the other will be 0.
   The 45° Rule: At a bearing of 045°, the Northing and Easting are identical.
   Rounding: Always round your final result to the nearest whole number before selecting a button.
   

Bearings & Navigation

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