New
New
Year 10
Foundation

Problem solving with right-angled trigonometry

I can use my knowledge of right-angled trigonometry to solve problems.

New
New
Year 10
Foundation

Problem solving with right-angled trigonometry

I can use my knowledge of right-angled trigonometry to solve problems.

Lesson details

Key learning points

  1. Sometimes an answer may be best left in an exact form
  2. When dealing with right-angled trigonometry, it is important to look at the information you have and can deduce
  3. Consider whether Pythagoras' theorem or trigonometric ratios are more efficient to use

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.

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.

You may wish to provide square grids for pupils to explore the area question in the first learning cycle.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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6 Questions

Q1.
Work out the length of the hypotenuse, to 1 decimal place.
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Correct Answer: 56.3 cm, 56.3
Q2.
Work out the length of the missing side of this right-angled triangle, to 1 decimal place.
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Correct Answer: 8.5 cm, 8.5
Q3.
Work out the length of the line segment AB, where A(2, 6) and B(5, 10).
Correct Answer: 5, five, 5 units
Q4.
Work out $$x$$ to 1 decimal place using the tangent ratio.
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Correct Answer: 8.7, 8.7 cm
Q5.
Work out the size of the angle, $$x$$.
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Correct Answer: 30, 30 degrees
Q6.
Work out the length of the edge marked $$x$$ to 1 decimal place.
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Correct Answer: 3.6 cm, 3.6

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.
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Correct Answer: 5.4, 5.4 units
Q2.
Which of these calculations are correct for finding the area of the square ABCD?
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Correct answer: $$7^2-4\times\left(\frac{2\times5}{2}\right)$$
$$2\times10+3^2$$
Correct answer: $$2^2+5^2$$
Correct answer: $$(\sqrt{2^2+5^2})^2$$
$$4\times\left(\frac{2\times5}{2}\right)-7^2$$
Q3.
Match the edge with the correct calculation.
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Correct Answer:AE,$$=\frac{16}{\tan(71.6^\circ)}$$

$$=\frac{16}{\tan(71.6^\circ)}$$

Correct Answer:DC,$$=\frac{16}{\sin(71.6^\circ)}$$

$$=\frac{16}{\sin(71.6^\circ)}$$

Correct Answer:FG,$$=HC+\frac{16}{\tan(71.6^\circ)}$$

$$=HC+\frac{16}{\tan(71.6^\circ)}$$

Q4.
Given that this is an isosceles triangle, calculate the angle marked $$x$$ to 1 decimal place.
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Correct Answer: 74.7, 74.7 degrees
Q5.
The area of this isosceles triangle is $$\text{cm}^2$$ to 3 significant figures.
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Correct Answer: 118
Q6.
Given that AB is the diameter of the circle, the area of the circle is $$\text{cm}^2$$ to 3 significant figures.
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Correct Answer: 331