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# GCSE Maths | Trigonometry
- URL: https://www.a-level-maths-tutor.com/gcse-maths-trigonometry/
- Published: 2026-08-03T14:16:28.000Z
- Updated: 2026-08-03T14:27:42.000Z
- Author: Jaisul Naik
- Tags: GCSE Maths

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/CleanShot-2026-02-12-at-16.47.14@2x.png)

### What is the sine rule?

**a/sin(A) = b/sin(B)**

**sin(A)/a = sin(B)/b**

### Question 1 - finding a length using the sine rule

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/CleanShot-2026-02-12-at-16.53.14@2x.png)

Show Answers 

**a)** $x = 6.39$ cm

**b)** $x = 6.65$ cm

**c)** $x = 60.5$ mm

### Question 2 - finding an angle using the sine rule

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/CleanShot-2026-02-12-at-16.54.17@2x.png)

Show Answers 

**a)** $\\theta = 37.1°$

**b)** $\\theta = 26.8°$

**c)** $\\theta = 40.5°$

### What is the cosine rule?

**a2 \= b2 \+ c2 \- 2bc cos(A)**

### Question 3 - finding a length using the cosine rule

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/CleanShot-2026-02-12-at-16.57.48@2x.png)

Show Answers 

**a)** $x = 9.17$ cm

**b)** $x = 30.41$ cm

**c)** $x = 36.67$ mm

### How do you rearrange the cosine rule to make cos(A) the subject?

**a2 \= b2 \+ c2 \- 2bc cos(A)**

**2bc cos(A)** \= **b2 \+ c2 \- a2** 

**cos(A) = (b2 \+ c2 \- a2)/2bc**

### Question 4 - finding an angle using the cosine rule

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/CleanShot-2026-02-12-at-16.58.07@2x.png)

Show Answers 

**a)** $\\theta = 49.5°$

**b)** $\\theta = 60.0°$

**c)** $\\theta = 87.2°$

### What is the area of any triangle?

**Area = (1/2) ab sin(C)**

### Question 5 - finding the area of any triangle

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/CleanShot-2026-02-12-at-16.59.20@2x.png)

Show Answers 

**a)** $45.0$ cm²

**b)** $156.32$ cm²

**c)** $52.62$ cm²

### Question 6 - using the area of a triangle to work out a missing length

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/CleanShot-2026-02-12-at-16.59.35@2x.png)

Show Answers 

**a)** $y = 8.51$ cm

**b)** $y = 6.96$ cm

**c)** $y = 7.95$ cm

### Question 7 - using the area of a triangle to work out a missing angle

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/02/CleanShot-2026-02-12-at-17.02.58@2x.png)

Show Answers 

**a)** $x = 78.9°$

**b)** $x = 31.6°$

**c)** $x = 30.0°$

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