At this point, you have multiple strategies available
By analysing the problem, you can determine which approach(es) might work
Keeping the goal in mind helps to focus your thinking
Consider the information you have and whether you need to know anything else in order to solve the problem
If you are unsure where to start, begin by calculating/deducing what you can

Common misconception

Pupils may be hesitant to start the problems due to uncertainty.

Encourage pupils to try an approach and then reflect on whether there has been progress towards a solution. Deducing something you didn't already know if progress even if it does not seem like it.

Keywords

Sine rule - The sine rule is a formula used for calculating either an unknown side length or the size of an unknown angle.
Cosine rule - The cosine rule is a formula used for calculating either an unknown side length or the size of an unknown angle.

Encourage pupils to solve the problems in multiple ways so that they can see which approaches do and do not work. Ask them to reflect on which method, if any, was better than the others.

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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Starter quiz

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6 Questions

Q1.

Match the correct rules, theorem or formulae.

Correct Answer:Pythagoras' theorem,$$a^2+b^2=c^2$$

$$a^2+b^2=c^2$$

Correct Answer:The sine rule,$$\frac{a}{\sin(A)}=\frac{b}{\sin(B)}=\frac{c}{\sin(C)}$$

$$\frac{a}{\sin(A)}=\frac{b}{\sin(B)}=\frac{c}{\sin(C)}$$

Correct Answer:The cosine rule,$$a^2 = b^2+c^2-2bc\cos(A)$$

$$a^2 = b^2+c^2-2bc\cos(A)$$

Correct Answer:Area of a triangle,$$\frac{1}{2}ab\sin(C)$$

$$\frac{1}{2}ab\sin(C)$$

Q2.

Given a triangle with lengths labelled $$a=8$$ cm, $$B=72$$° and $$c=12$$ cm work out length $$b$$ cm.

19.2 cm

Correct answer: 12.2 cm

8.4 cm

4.2 cm

10.8 cm

Q3.

Given a triangle with lengths labelled $$a=32$$ cm, $$b=24$$ cm and $$c=40$$ cm, work out angle $$B$$.

12.39°

53.13°

Correct answer: 36.87°

80.32°

94.54°

Q4.

A plane starts at City X and flies 4 km due north to City A, then turns at a bearing of 068 for 10.8 km to City B. If the plane flew directly from City X to City B, what is the distance?

10.2 km

Correct answer: 12.8 km

13.4 km

19.8 km

Q5.

A plane starts at an airport and then travels North 8 km, then North East 4.2 km. What is the distance the plane needs to travel to get back to the airport?

Correct Answer: 11.4 km, 11.4

Q6.

A plane starts at an airport and then travels North 8 km, then North East 4.2 km. What is the bearing the plane needs to travel at to get back to the airport?

Correct answer: 195°

204°

206°

207°

302°

Exit quiz

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6 Questions

Q1.

Which of these formulae are the correct rearrangements where the subject of the formula is a length?

$$a^2=b^2+c^2-2bc\cos(A)$$

$$b^2=a^2+c^2-2ac\cos(B)$$

Correct answer: $$a=\frac{b\times\sin(A)}{\sin(B)}$$

$$\cos(A)=\frac{b^2+c^2-a^2}{2bc}$$

$$\sin(A)=\frac{a\times\sin(B)}{b}$$

Q2.

Which of these formulae are the correct rearrangements where the subject of the formula is angle $$A$$?

$$a^2=b^2+c^2-2bc\cos(A)$$

$$a=\frac{b\times\sin(A)}{\sin(B)}$$

Correct answer: $$A=\cos^{-1}\left(\frac{b^2+c^2-a^2}{2bc}\right)$$

$$\cos(A)=\frac{a^2+b^2-a^2}{2ab}$$

Correct answer: $$A=\sin^{-1}\left(\frac{a\times\sin(B)}{b}\right)$$

Q3.

Given a triangle with vertices labelled $$A$$, $$B$$ and $$C$$, how do you know you are able to use the sine rule?

Correct answer: When you have two pairs of opposites, where one value in a pair is unknown

When three lengths of the triangle are given

When two adjacent lengths and the angle in between are given

When 3 angles are given

Q4.

Given a triangle with vertices labelled $$A$$, $$B$$ and $$C$$, how do you know you are able to use the cosine rule?

When you have two pairs of opposites, where one value in a pair is unknown

Correct answer: When three lengths of the triangle are given

Correct answer: When two adjacent lengths and the angle in between are given

When 3 angles are given

Q5.

A triangle has 3 vertices, $$A$$, $$B$$ and $$C$$. It also has the corresponding lengths $$a$$, $$b$$ and $$c$$. When $$a$$ = 8.25 cm, $$C$$ = 76.0°, $$b$$ = 8 cm, work out the perimeter.

Correct answer: 26.26 cm

30.75 cm

39.76 cm

48.25 cm

Q6.

A triangle has vertices, $$N$$, $$L$$ and $$M$$. It has corresponding lengths $$n$$, $$l$$ and $$m$$. When $$M = 94.4°, n = 8.9$$ cm, $$N = 53.8°$$ and $$l = 5.8$$ cm, work out the perimeter (1 d.p.).

Correct Answer: 25.7 cm, 25.7