Bearings – Applications of the sine and cosine rules

Bearings – Applications of the sine and cosine rules

Bearings

• Bearings are a type of angle used to denote direction in navigation and geography.
• They are always measured from the North line, which represents the 0-degree point, in a clockwise direction.
• A bearing is typically a three-digit value, with the number of degrees between 000 and 360.

Sine and Cosine Rules

• Sine rule is applied when we have either “two angles and one side” or “two sides and a non-included angle” conditions available in a triangle.
• Cosine rule is used when we have the “three sides” or “two sides and the included angle” condition in a triangle.

Applications of Sine and Cosine Rules in Bearings

• Bearings problems often involve right-angled or non-right-angled triangles, and the sine or cosine rule can be used to solve for missing components.
• If the triangle associated with the bearings problem is not a right triangle, use the sine rule or the cosine rule.
• If a right-angled triangle is involved, trigonometric functions come into play, involving sine, cosine, and tangent, and their inverse functions.

Practical Applications

• Understanding bearings and the application of the sine and cosine rules are crucial in areas such as navigation, civil engineering, map reading, and even in programming for game development.
• Mastery of these concepts and rules will help accurately find distances and directions, enhancing navigational and locational abilities.

As you revise these concepts, always remember to identify if a bearings problem involves a right triangle or not and, based on this, decide which rule to apply. Regular practice will fortify these concepts and rules, enabling swift and accurate solving of bearings problems.