Myths about teaching can hold you back
- Year 10•
- Foundation
Checking and securing understanding of tangent ratio problems
I can use the tangent ratio to find the missing side or angle in a right-angled triangle.
- Year 10•
- Foundation
Checking and securing understanding of tangent ratio problems
I can use the tangent ratio to find the missing side or angle in a right-angled triangle.
Lesson details
Key learning points
- The tangent ratio involves the opposite, adjacent and the angle
- If you know the length of the opposite and the size of the angle, you can use the tangent ratio
- If you know the length of the adjacent and the size of the angle, you can use the tangent ratio
- If you know the length of the opposite and adjacent, you can use the tangent ratio
Keywords
Trigonometric functions - Trigonometric functions are commonly defined as ratios of two sides of a right-angled triangle containing the angle.
Tangent function - The tangent of an angle (tan(θ°)) is the y-coordinate of point Q of the triangle which extends from the unit circle.
Adjacent - The adjacent side of a right-angled triangle is the side which is next to both the right angle and the marked angle.
Opposite - The opposite side of a right-angled triangle is the side which is opposite the marked angle.
Common misconception
Pupils may confuse the opposite and adjacent sides.
The orientation of the right-angled triangle is not important. Identifying the known angle is what determines which is is the opposite and which is the adjacent.
To help you plan your year 10 maths lesson on: Checking and securing understanding of tangent ratio 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 tangent ratio 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.Match the names of the sides, relative to the angle $$\theta$$.
a -
opposite
b -
adjacent
c -
hypotenuse
Q2.The two triangles are similar. What is the length of $$x$$?
Q3.Triangle ABC and triangle DEF are similar. What is the length of $$x$$?
Q4.Work out the value of $$x$$ to 3 significant figures.
Q5.Work out the value of $$x$$ to 1 decimal place.
Q6.Work out the length of $$x$$, to 1 decimal place.
Assessment exit quiz
6 Questions
Q1.For a right-angled triangle, the tangent ratio is $$\tan(\theta)=\frac{\text{opp}}{\text{adj}}$$, where $$\theta$$ is the angle in degrees. Which of these are equivalent forms?
Q2.Work out the length of $$x$$, to 1 decimal place.
Q3.Work out the length of $$x$$, to 1 decimal place.
Q4.Using the table of values, what is the value of $$\theta$$?
Q5.Match the variables to their values.
opposite -
33
adjacent -
48
theta -
34.50852299
Q6.Work out the value of $$\theta$$, to the nearest degree.
