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- Year 10•
- Higher
Advanced problem solving with right-angled trigonometry
I can use my knowledge of right-angled trigonometry to solve problems.
- Year 10•
- Higher
Advanced problem solving with right-angled trigonometry
I can use my knowledge of right-angled trigonometry to solve problems.
Lesson details
Key learning points
- Sometimes an answer may be best left in an exact form
- When dealing with right-angled trigonometry, it is important to look at the information you have and can deduce
- Consider whether Pythagoras' theorem or trigonometric ratios are more efficient to use
- All models are wrong, but some models are useful
Keywords
Trigonometric functions - Trigonometric functions are commonly defined as ratios of two sides of a right-angled triangle for a given angle.
Sine function - The sine of an angle (sin(θ°)) is the y-coordinate of point P on the triangle formed inside the unit circle.
Cosine function - The cosine of an angle (cos(θ°)) is the x-coordinate of point P on the triangle formed inside the unit circle.
Tangent function - The tangent of an angle (tan(θ°)) is the y-coordinate of point Q on the triangle which extends from the unit circle.
Common misconception
Pupils may not be confident in knowing whether to apply Pythagoras' theorem or a trigonometric ratio.
Encourage pupils to label the diagram with all the information they have and then consider what they can deduce.
To help you plan your year 10 maths lesson on: Advanced problem solving with right-angled trigonometry, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 10 maths lesson on: Advanced problem solving with right-angled trigonometry, 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.
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Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.Work out the length of the hypotenuse, to 1 decimal place.
Q2.Work out the length of the missing side of this right-angled triangle, to 1 decimal place.
Q3.Work out the length of the line segment AB, where A(-2, -6) and B(1, -10).
Q4.Work out $$x$$ to 1 decimal place.
Q5.Work out the size of the angle, $$x$$, to 1 decimal place.
Q6.Work out the length of the edge marked $$x$$ to 1 decimal place.
Assessment exit quiz
6 Questions
Q1.ABCD is a square on a grid, where each square is 1 unit. Work out the length of BC, to 1 decimal place.
Q2.The exact area of the square ABCD is square units.
Q3.Work out the length of CD correct to 1 decimal place.
Q4.Work out the perpendicular height of this isosceles triangle, to 1 decimal place.
Q5.Given that FE = 12 cm, EH = 19 cm and angle DHE = $$40^\circ$$, calculate the volume of the cuboid ABCDEFGH, to the nearest integer.
Q6.Match the parts of the cylinder to the correct calculation/answer.
radius of the cylinder -
$$=18\cos(62^\circ)$$
length of the cylinder -
$$=18\cos(28^\circ)$$
volume of the cylinder -
$$=(18\sin(28^\circ))^2\times\pi\times18\cos(28^\circ)$$
diameter of the cylinder -
16.9 cm (3 s.f.)