The cosine rule
I can derive the formula for the cosine rule.
The cosine rule
I can derive the formula for the cosine rule.
These resources will be removed by end of Summer Term 2025.
Lesson details
Key learning points
- There are multiple ways to prove the cosine rule
- When deriving (or proving) it is sometimes useful to derive other information
Keywords
Cosine rule - The cosine rule is a formula used for calculating either an unknown side length or the size of an unknown angle.
Common misconception
Pupils may not see the need for this rule as they have the sine rule.
The sine rule can be used in many cases but it is not always the most efficient. There will be problems where it will be much faster to use the cosine rule.
To help you plan your year 11 maths lesson on: The cosine rule, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 11 maths lesson on: The cosine rule, download all teaching resources for free and adapt to suit your pupils' needs.
The starter quiz will activate and check your pupils' prior knowledge, with versions available both with and without answers in PDF format.
We use learning cycles to break down learning into key concepts or ideas linked to the learning outcome. Each learning cycle features explanations with checks for understanding and practice tasks with feedback. All of this is found in our slide decks, ready for you to download and edit. The practice tasks are also available as printable worksheets and some lessons have additional materials with extra material you might need for teaching the lesson.
The assessment exit quiz will test your pupils' understanding of the key learning points.
Our video is a tool for planning, showing how other teachers might teach the lesson, offering helpful tips, modelled explanations and inspiration for your own delivery in the classroom. Plus, you can set it as homework or revision for pupils and keep their learning on track by sharing an online pupil version of this lesson.
Explore more key stage 4 maths lessons from the Non right-angled trigonometry unit, dive into the full secondary maths curriculum, or learn more about lesson planning.
Licence
Lesson video
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Starter quiz
6 Questions
The sine of an angle is the -
$$y$$-coordinate of P on the triangle formed inside the unit circle.
The cosine of an angle is the -
$$x$$-coordinate of P on the triangle formed inside the unit cirlce.
The tangent is the -
line that intersects the circle exactly once.
1 -
$$\cos(0°)$$
$$\frac{\sqrt{3}}{2}$$ -
$$\cos(30°)$$
$$\frac{\sqrt{2}}{2}$$ -
$$\cos(45°)$$
0.5 -
$$\cos(60°)$$
0 -
$$\cos(90°)$$
-0.174 (3 s.f) -
$$\cos(100°)$$
Exit quiz
6 Questions
Pythagoras' theorem -
$$a^2+b^2=c^2$$
The sine rule -
$$\frac{a}{\sin(A)}=\frac{b}{\sin(B)}=\frac{c}{\sin(C)}$$
The cosine rule -
$$a^2 = b^2+c^2-2bc\cos(A)$$
Area of a triangle -
$$\frac{1}{2}ab\sin(C)$$
10.6 cm -
$$a=8$$ cm, $$B=36$$° and $$c=16$$ cm
11.8 cm -
$$a=16$$ cm, $$B=36$$° and $$c=20$$ cm
4.9 cm -
$$a=8$$ cm, $$B=36$$° and $$c=8$$ cm
12.2 cm -
$$a=8$$ cm, $$B=72$$° and $$c=12$$ cm
46.57° -
$$a=8$$ cm, $$b=12$$ cm and $$c=16$$ cm
36.87° -
$$a=16$$ cm, $$b=12$$ cm and $$c=20$$ cm
97.18° -
$$a=8$$ cm, $$b=12$$ cm and $$c=8$$ cm
70.53° -
$$a=8$$ cm, $$b=12$$ cm and $$c=12$$ cm