MA30-03 Maths Coming soon
Using trigonometry to find missing sides and angles
This lesson is coming soon.
In this lesson
Use sin, cos or tan to calculate a missing side or angle in a right-angled triangle, including problems that require Pythagoras and trigonometry together in the same figure, and 'show that' questions that must be worked forwards.
What it covers
- Recognise when a right-angled-triangle problem needs trigonometry: one side and one angle known, a second side or an angle wanted
- Set up and solve sin/cos/tan as an equation to find a missing side
- Set up and solve sin/cos/tan, using the inverse function, to find a missing angle
- A combined 2D problem where Pythagoras finds one length and trigonometry then finds an angle (or a further length) in the same figure
- 'Show that' questions: deriving the target value by working forward from the given information, never starting from the value to be shown
Key words
For: Cambridge IGCSE 0580, Edexcel IGCSE 4MA1, AQA GCSE 8300, Edexcel GCSE 1MA1, Eduqas GCSE C300, OCR GCSE J560
On the specification
| Board | Spec | Statement |
|---|---|---|
| Cambridge IGCSE 0580 | C6.2 | Know and use the sine, cosine and tangent ratios for acute angles in calculations involving sides and angles of a right-angled triangle. |
| Cambridge IGCSE 0580 | E6.2 | Know and use the sine, cosine and tangent ratios for acute angles in calculations involving sides and angles of a right-angled triangle. |
| Edexcel IGCSE 4MA1 | F4.8B | Know, understand and use sine, cosine and tangent of acute angles to determine lengths and angles of a right-angled triangle |
| Edexcel IGCSE 4MA1 | F4.8C | Apply trigonometrical methods to solve problems in two dimensions |
| AQA GCSE 8300 | G20 | Know the formulae for: Pythagoras’ theorem, a² + b² = c² and the trigonometric ratios, sinθ = opposite/hypotenuse, cosθ = adjacent/hypotenuse and tanθ = opposite/adjacent |
| Edexcel GCSE 1MA1 | G20 | Know the formulae for: Pythagoras’ theorem a² + b² = c², and the trigonometric ratios, sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse and tan θ = opposite/adjacent; apply them to find angles and lengths in right-angled triangles in two-dimensional figures |
| Eduqas GCSE C300 | FG18 | Know the formulae for: Pythagoras' theorem, a² + b² = c², and the trigonometric ratios, sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent; apply them to find angles and lengths in right-angled triangles in two dimensional figures |
| OCR GCSE J560 | 10.05b | Know and apply the trigonometric ratios, sin θ, cos θ and tan θ and apply them to find angles and lengths in right-angled triangles in 2D figures. |
For teachers
This GCSE Maths lesson teaches using trigonometry to find missing sides and angles. By the end, students should be able to use sin, cos or tan to calculate a missing side or angle in a right-angled triangle, including problems that require Pythagoras and trigonometry together in the same figure, and 'show that' questions that must be worked forwards. It works through three worked examples and the mistakes examiners report.