I need to match each triangle diagram with the correct trigonometric rule. Let me analyze each triangle based on what information is given (marked sides and angles).
Triangle 1: Two sides marked, included angle marked
- We have two sides and the angle between them
- This calls for the cosine rule: cos A = (b² + c² - a²)/(2bc)
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Match: Use the cosine rule cos A = (b² + c² - a²)/(2bc)
Triangle 2: One side marked, two angles marked
- We have one side and two angles
- We can use the sine rule twice to find both missing sides
- Or use sine rule once then cosine rule
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Match: Use the sine rule twice, or sine rule followed by the cosine rule
Triangle 3: Two angles marked, no sides marked
- We only have angles, no side lengths
- We can use the sine rule to find ratios between sides
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Match: Use the sine rule a/sin A = b/sin B
Triangle 4: Three sides marked, no angles marked
- We have all three sides but no angles
- We can use the cosine rule to find any angle
- The form a² = b² + c² - 2bc cos A rearranges to find an angle
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Match: Use the cosine rule a² = b² + c² - 2bc cos A
Triangle 5: Two sides marked, one non-included angle marked
- We have two sides and an angle not between them
- We can use the sine rule to find another angle
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Match: Use the sine rule sin A/a = sin B/b
Triangle 6: Two angles marked, one side marked
- We have two angles and one side
- We can find the third angle (angles sum to 180°), then use sine rule
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Match: Use the sine rule to find the other missing angle and then subtract both known angles from 180°
Final Answer:
1. Triangle with 2 sides + included angle → Use the cosine rule cos A = (b² + c² - a²)/(2bc)
2. Triangle with 1 side + 2 angles → Use the sine rule twice, or sine rule followed by the cosine rule
3. Triangle with 2 angles only → Use the sine rule a/sin A = b/sin B
4. Triangle with 3 sides → Use the cosine rule a² = b² + c² - 2bc cos A
5. Triangle with 2 sides + non-included angle → Use the sine rule sin A/a = sin B/b
6. Triangle with 2 angles + 1 side → Use the sine rule to find the other missing angle and then subtract both known angles from 180°
Parent Tip: Review the logic above to help your child master the concept of geometry trig worksheet.
