Video 8: True Bearings

True Bearings Explained

Introduction to True Bearings

• Natalie McClatchy introduces the topic of true bearings as part of a series on Pythagoras theorem and trigonometry, aimed at students in grades 9 to 12.

• The video will cover definitions, how to find true bearings, conversions between compass and true bearings, reverse bearings, and a worded problem.

What is a True Bearing?

• True bearings are measured clockwise from north and expressed as three-digit numbers with "degrees true" (e.g., 070°T).

• A bearing of 70 degrees true indicates an angle of 70 degrees clockwise from north towards the object being observed.

• True bearings range from 0° to 360°, meaning there are no negative values or values exceeding this range.

Worked Examples: Finding True Bearings

• In the first example, standing at point O looking towards point A requires calculating the angle between north and A. Given an external angle of 35°, the true bearing is found by subtracting it from 90°, resulting in a bearing of 55°T.

• For point B with a given angle of 17°, the calculation involves subtracting this value from 180° (the straight line), yielding a true bearing of 163°T.

• Another example involves finding the bearing for point C by adding angles quadrant-wise: North (90°), East (90°), plus an additional angle gives us a total of 191°T.

Converting Between Compass Bearings and True Bearings

• To convert a compass bearing like South 42° East into a true bearing, one must visualize it on a compass diagram. This results in calculating angles based on known right angles.

• The conversion process leads to determining that South 42° East corresponds to a true bearing of approximately 138°T.

Understanding Forward vs. Reverse Bearings

• The difference between forward and reverse bearings is crucial; they differ by exactly 180°.

• If given a forward bearing (e.g., +2°), its reverse would be calculated as +2 -180 = -178°, which isn't valid; thus we add instead: +2 +180 = +182°.

• Conversely, if starting with an already high forward bearing like +200°, subtracting yields valid results within bounds.

Proving Reverse Bearing Calculations

• An example demonstrates finding the reverse bearing using triangle properties. From O to D yields one angle while D back to O provides another distinct measurement.

• Ultimately proving that forward and reverse bearings maintain their relationship through consistent calculations shows that they always differ by exactly ±180°.

Practical Application: Word Problem Example

• A scenario involving hiking illustrates practical application where distance traveled at specific angles needs resolving into components using trigonometric ratios.

• By drawing diagrams and applying cosine formulas, one can determine distances southward versus eastward effectively.

Conclusion & Future Topics

• Upcoming videos will explore non-right-angle triangles using trigonometry along with more complex problems integrating previous lessons learned about true bearings.