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GCSE Sine Rule Questions and Answers

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Question 22 - AQA GCSE Higher Maths Past Paper 1 November 2021

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Sine Rule

1. Introduction.

To find the missing angles and sides of a right angled triangle we can apply trigonometric ratios SOH CAH TOA.  However to find the missing sides and angles of other triangles we apply sine rule. Let us learn about sine rule.

1.1 What is the Sine Rule?

The sine rule is a relationship between the size of an angle in a triangle and the opposing side. Sine rule helps in finding any missing side or angle of a triangle. The sine rule is used when we are given either a) two angles and one side, or b) two sides and a non-included angle.

Sine Rule:

01. Sine rule

It depends on the missing angle and the sides of the triangle which two of them of sine rule to be used. For example in the triangle below, b/Sin B = c/Sin C are used to find missing side c.

02. Sine rule

Note: Angles are denoted with Capital letters, while sides with lower case.

1.2 How to use the sine rule?

In order to apply the Sine rule, first label the missing sides and angles. The opposite angle is the same letter as the opposite side. Next apply the  sine rule to find the missing side or angle.

While solving using the sine rule one can rewrite the formula based on the question. For example, to find missing length apply the same formula. But for finding missing  angle, you can use the version where angles are in numerator.,

 Sin A/a = Sin B/b = Sin C/c

Remember that each fraction in the Sine Rule formula should contain a side and its opposite angle.

Example 1: Finding a missing side of a triangle

In the given triangle Side AC = 6 cm, angle ABC = 60° and angle ACB =70°. Calculate the side AB.

03. Sine rule

Solution:

GCSE Sine Rule Solution 01

Example 2: Finding a missing angle of a triangle

In the given triangle sides, a = 8 cm, b = 6 cm, and c = 2 cm and angle ACB= 10°. Calculate angle BAC 

04. Sine rule

Solution:

GCSE Sine Rule Solution 02

Example 3:

In triangle ABC, B = 21◦ , C = 46◦ and AB = 9cm. Solve this triangle for side AC

Solution:

GCSE Sine Rule Solution 03

05. Sine rule

GCSE Sine Rule Solution 03b

Quiz Questions

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GCSE Topics

  • Probability (258)
  • Statistical Measures (5)
  • Numbers (1,084)
  • Data Visualisation (4)
  • Algebra (1,176)
  • Ratio, Proportion and Rates of Change (443)
  • Geometry and Measures (809)
  • Statistics (274)
    • Frequently Asked Questions
    What are the main topics in GCSE Maths?

    The main topics in GCSE Maths are:

    • Numbers
    • Algebra 
    • Ratio, Proportion and Rates of Change 
    • Geometry and Measures
    • Statistics 
    • Probability 
    • Statistical Measures 
    • Data Visualisation 

    With regular practice of GCSE Maths topic-wise questions and GCSE Maths past pacers, you can easily score high marks.

    Is GCSE Maths hard?

    Although many people think of GCSE maths as a difficult subject, with the correct training and preparation,you can master it in time. You can practice GCSE Maths  topic-wise questions daily to improve speed, accuracy, and time and to score high marks in the GCSE Maths exam.

    What is a good grade on GCSE Maths Exam?

    A grade of 4 or 5 would be considered "good" because the government has established a 4 as the passing grade; a grade of 5 is seen as a strong pass. Therefore, anything that exceeds this level would be considered good. You can practice GCSE Maths topic-wise questions to score good grades in the GCSE Maths exam.

    How can I get full marks in GCSE Maths?

    You can get a high score in GCSE Maths through meticulous practice of GCSE Maths topic-wise questions and GCSE Maths past papers.

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