MA30-05 Maths Coming soon
The sine rule and the area of a triangle
MA30-05
This lesson is coming soon.
In this lesson
Recognise when a triangle is not right-angled, use the sine rule to find a missing side or angle, and use Area = ½ab sinC to find the area of any triangle.
What it covers
- Recognise a non-right-angled (scalene) triangle as a signal that SOHCAHTOA does not apply
- State the sine rule a/sinA = b/sinB = c/sinC and use it to find a missing side
- Rearrange the sine rule to find a missing angle
- Chain the sine rule with the angle-sum-of-a-triangle fact (180 degrees) to find a second unknown angle in a two-stage problem
- Use Area = ½ab sinC to find the area of a triangle when two sides and the included angle are known, including deciding which angle to work with first when it isn't handed over directly
Key words
For: Edexcel IGCSE 4MA1, Cambridge IGCSE 0580, AQA GCSE 8300, Edexcel GCSE 1MA1, Eduqas GCSE C300, OCR GCSE J560
On the specification
| Board | Spec | Statement |
|---|---|---|
| Edexcel IGCSE 4MA1 | H4.8C | Understand and use the sine and cosine rules for any triangle |
| Edexcel IGCSE 4MA1 | H4.8E | Understand and use the formula 1/2 ab sin C for the area of a triangle |
| Cambridge IGCSE 0580 | C6.5 | Extended content only. |
| Cambridge IGCSE 0580 | E6.5 | Use the sine and cosine rules in calculations involving lengths and angles for any triangle. |
| AQA GCSE 8300 | G22 | Know and apply the sine rule, a/sinA = b/sinB = c/sinC and cosine rule, a² = b² + c² - 2bc cosA to find unknown lengths and angles |
| AQA GCSE 8300 | G23 | Know and apply Area = ½ ab sinC to calculate the area, sides or angles of any triangle |
| Edexcel GCSE 1MA1 | G22 | Know and apply the sine rule a/sin A = b/sin B = c/sin C, and cosine rule a² = b² + c² − 2bc cos A, to find unknown lengths and angles |
| Edexcel GCSE 1MA1 | G23 | Know and apply Area = ½ ab sin C to calculate the area, sides or angles of any triangle |
| Eduqas GCSE C300 | HG22 | Know and apply the sine rule, a/sin A = b/sin B = c/sin C, and cosine rule, a² = b² + c² − 2bc cos A, to find unknown lengths and angles |
| Eduqas GCSE C300 | HG23 | Know and apply Area = ½ ab sin C to calculate the area, sides or angles of any triangle |
| OCR GCSE J560 | 10.05e | Know and apply the cosine rule, a^2 = b^2 + c^2 - 2bc cos A, to find lengths and angles. |
| OCR GCSE J560 | 10.05d | Know and apply the sine rule, a/sin A = b/sin B = c/sin C , to find lengths and angles. |
| OCR GCSE J560 | 10.03a | Know and apply the formula: area = 1/2 base × height. |
For teachers
This GCSE Maths lesson teaches the sine rule and the Area of a triangle. By the end, students should be able to recognise when a triangle is not right-angled, use the sine rule to find a missing side or angle, and use Area = ½ab sinC to find the area of any triangle. It works through three worked examples and the mistakes examiners report.