Myths about teaching can hold you back
- Year 10•
- Higher
Checking and securing understanding of cosine problems
I can use the cosine ratio to find the missing side or angle in a right-angled triangle.
- Year 10•
- Higher
Checking and securing understanding of cosine problems
I can use the cosine ratio to find the missing side or angle in a right-angled triangle.
Lesson details
Key learning points
- The cosine ratio involves the hypotenuse, adjacent and the angle
- If you know the length of the hypotenuse and the size of the angle, you can use the cosine ratio
- If you know the length of the adjacent and the size of the angle, you can use the cosine ratio
- If you know the length of the hypotenuse and adjacent, you can use the cosine ratio
Keywords
Hypotenuse - The hypotenuse is the side of a right-angled triangle which is opposite the right angle.
Adjacent - The adjacent side of a right-angled triangle is the side which is next to both the right angle and the marked angle.
Trigonometric functions - Trigonometric functions are commonly defined as ratios of two sides of a right-angled triangle containing the angle.
Cosine function - The cosine of an angle (cos(θ°)) is the x-coordinate of point P on the triangle formed inside the unit circle.
Common misconception
The cosine formula is only used to find the length of a side adjacent to an angle.
The cosine formula can be used to find the length of a side adjacent to an angle. A rearrangement of the formula also allows us to find the length of the hypotenuse given the adjacent side. The arccosine function allows us to find the angle, itself.
To help you plan your year 10 maths lesson on: Checking and securing understanding of cosine problems, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 10 maths lesson on: Checking and securing understanding of cosine problems, 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 Right-angled trigonometry unit, dive into the full secondary maths curriculum, or learn more about lesson planning.
Licence
Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.Two shapes are similar if the only difference between them is their . Their side lengths are in the same proportions.
Q2.Triangle ABC and triangle DEF are similar. What is the length of side $$x$$?
Q3.Triangle ABC and triangle DEF are similar. What is the length of side $$x$$?
Q4.The two triangles are similar. What is the size of the angle marked $$x$$?
Q5.What is the approximate value of $$\cos(60^\circ)$$?
Q6.What is the approximate value of $$\cos(30^\circ)$$?
Assessment exit quiz
6 Questions
Q1.Work out the length of $$x$$, given that these two triangles are similar.
Q2.Work out the length of $$x$$, given that these two triangles are similar.
Q3.For a right-angled triangle, the cosine ratio is $$\cos(\theta)=\frac{\text{adj}}{\text{hyp}}$$, where $$\theta$$ is the angle in degrees. Which of these are equivalent forms?
Q4.Which of the following equations are correct when finding the angle $$n^\circ$$ in the equation: $$\cos(n^\circ)=0.57$$?
Q5.Which of these is correct for this triangle?
Q6.Calculate the length of $$x$$ to 2 decimal places.
