Page 1: Triangle Problem-Solving Methods

This page provides detailed explanations of when and how to use sine and cosine rules in different triangle scenarios.

Definition: The sine rule is used when you have either two angles and any side, or two sides and a non-enclosed angle. The cosine rule is used when you have three sides or two sides and their enclosed angle.

Example: For a triangle with angles 83° and 53° and a side of 7m, using sine rule: $7/sin(44°)$ × sin(53°) = 8.05m

Highlight: When using the sine rule, remember that it always provides an acute angle. If the angle you're finding is obtuse, subtract the result from 180°.

Vocabulary:

• Enclosed angle: The angle formed between two given sides of a triangle
• Obtuse angle: An angle greater than 90° but less than 180°
• Acute angle: An angle less than 90°

The page demonstrates four key scenarios:

1. Using sine rule with two angles and one side
2. Applying cosine rule with two sides and enclosed angle
3. Implementing sine rule with two sides and non-enclosed angle
4. Utilizing cosine rule when all three sides are given

Quote: "The sine rule will always give you an acute angle - if the angle you're finding is obtuse, subtract the angle from 180°"