Considering the appropriate trigonometric rule | Maths

Starter quiz

Match the correct rules, theorem or formulae.

Pythagoras' theorem

⇔

$a^2+b^2=c^2$ ✓

The sine rule

⇔

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

The cosine rule

⇔

$a^2 = b^2+c^2-2bc\cos(A)$ ✓

Area of a triangle

⇔

$\frac{1}{2}ab\sin(C)$ ✓
Given a triangle with lengths labelled $a=8$ cm, $B=72$ ° and $c=12$ cm work out length $b$ cm.

19.2 cm

12.2 cm ✓

8.4 cm

4.2 cm

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

12.39°

53.13°

36.87° ✓

80.32°

94.54°
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

12.8 km ✓

13.4 km

19.8 km
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?

'11.4 km' ✓
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?

195° ✓

204°

206°

207°

302°

Exit quiz

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

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

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

$a=\frac{b\times\sin(A)}{\sin(B)}$ ✓

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

$\sin(A)=\frac{a\times\sin(B)}{b}$
Which of these formulae are the correct rearrangements where the subject of the formula is angle $A$ ?

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

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

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

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

$A=\sin^{-1}\left(\frac{a\times\sin(B)}{b}\right)$ ✓
Given a triangle with vertices labelled $A$ , $B$ and $C$ , how do you know you are able to use the sine rule?

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
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

When three lengths of the triangle are given ✓

When two adjacent lengths and the angle in between are given ✓

When 3 angles are given
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.

26.26 cm ✓

30.75 cm

39.76 cm

48.25 cm
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.).

'25.7 cm' ✓

Worksheet

Loading worksheet ...

Presentation

Loading presentation ...

Video

Lesson Details

Key learning points

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.