New
New
Year 11
Higher

Problem solving with non right-angled trigonometry

I can use my knowledge of trigonometry to solve problems.

New
New
Year 11
Higher

Problem solving with non right-angled trigonometry

I can use my knowledge of trigonometry to solve problems.

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Lesson details

Key learning points

  1. Non right-angled trigonometry can be applied in various contexts
  2. It has the potential to be applied whenever a triangle can be drawn

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 think that they have to use the sine or cosine rule.

Encourage pupils to consider all the trigonometric knowledge they have and choose the most appropriate piece for the problem they are dealing with.

Pupils can feel overwhelmed with choice so it is helpful to allow the to see that multiple approaches can often be taken. Therefore it does not matter which of the various appropriate approaches they went for.
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).

Lesson video

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6 Questions

Q1.
Trigonometric functions are commonly defined as __________ of two sides of a right-angled triangle for a given angle.
Correct answer: ratios
examples
particles
difference
Q2.
Which of these formulae are the sine rule or correct rearrangements of the sine rule?
Correct answer: $$\sin(A)=\frac{a\sin(B)}{b}$$
Correct answer: $$\frac{b}{\sin(b)}=\frac{c}{\sin(C)}$$
Correct answer: $$\frac{a}{\sin(A)}=\frac{c}{\sin(C)}$$
Correct answer: $$\frac{a}{\sin(A)}=\frac{b}{\sin(B)}=\frac{c}{\sin(C)}$$
$$\frac{a}{\sin(b)}=\frac{b}{\sin(C)}$$
Q3.
A triangle has vertices $$A, B$$ and $$C$$, and corresponding lengths $$a, b$$ and $$c$$. $$C$$ = 39.6°, $$c$$ = 6.4 cm and $$a$$ = 9.4 cm. Work out acute angle $$A$$ to 1 significant figure.
Correct Answer: 70°, 70 degrees, 70
Q4.
An isosceles triangle has two lengths of 9.22 cm and the third length 14 cm. Work out the angle between the two equal lengths. Give your answer to 1 decimal place.
Correct Answer: 98.8°, 98.8 degrees, 98.8
Q5.
An isosceles triangle with lengths 8.6 cm, 8.6 cm and $$x$$ cm has two base angles of 54.5°. Work out the perimeter of the triangle to 1 decimal place.
Correct Answer: 27.2 cm, 27.2
Q6.
The area of a regular hexagon is 93.5 cm$$^2$$. Work out the perimeter of the regular hexagon to the nearest integer.
Correct Answer: 36 cm , 36

6 Questions

Q1.
A square has a diagonal length of 8.49 cm. The area of the square, to the nearest integer, is cm$$^2$$.
Correct Answer: 36
Q2.
A rectangle has two diagonals. The length of each diagonal is 13.4 cm. The diagonals intersect to create two obtuse angles of 127°. Work out the longest length of the rectangle to 2 s.f.
Correct Answer: 12 cm, 12
Q3.
A rectangle has two diagonals. The length of each diagonal is 13.4 cm. The diagonals intersect to create two obtuse angles of 127°. Work out the perimeter to the nearest integer.
Correct Answer: 36 cm , 36
Q4.
A rectangle has two diagonals. The length of each diagonal is 9.5 cm. The diagonals intersect to create two obtuse angles of 143°. Work out the perimeter to the nearest integer.
Correct Answer: 24 cm, 24
Q5.
A triangle has three lengths; 11.3 cm, 12.7 cm and 17.0 cm. Identify the three angles.
Correct answer: 90°, 48.3° and 41.7°
48.4°, 81° and 50.6°
41.6°, 53.5° and 84.9°
90°, 34° and 56°
Q6.
A triangle has three lengths; 10.3 cm, 15.8 cm and 8 cm. Identify the three angles when rounded to 3 s.f.
Correct answer: 119°, 26.3° and 34.8°
119°, 30° and 31°
26.3°, 40.5° and 113.2°
34.7°, 56.9° and 88.4°