1. Know and apply the sine rule to find unknown lengths and angles
Grade 7/8
Sine Rule
Know and apply the sine rule to find unknown lengths and angles
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2. Lesson Plan Lesson Overview Progression of Learning
Objective(s)
Know and apply the sine rule to find unknown lengths and angles
Grade
7/8
Prior Knowledge
Side/angle notation
Substituting, rearranging and solving equations
Rounding
Sine function
Duration
30 minutes
Resources
Print slides:
Equipment
Calculator
Progression of Learning
What are the students learning?
How are the students learning? (Activities & Differentiation)
Introduce the formula for sine rule
Give students slide 12. Using slide 4 show the formula – remind students that this will not be given to them in the exam therefore they must memorise. 5
Deciding when the sine rule can be used
Using the triangle diagrams on slide 4 explain when the sine rule is used. Students to practice – give students slide 13. Review answers on slide 5. When discussing the answers mention if finding a missing side or angle and why.
Using slide 6 review the formula again and the steps to follow when answering a question.
Application of sine rule to find missing side and missing angle
Give students slide 14. Using slide 7 and 8 show the steps for applying the sine rule. Give students slide 15 and 16 this includes 6 questions to practice. Review answers collectively using slide 9 and 10. 15
Application of sine rule in contextualised problems
Give students slide 17. Students to apply knowledge from lesson to answer this problem.
Using the sine rule in exam questions (from specimen papers)
Note that almost all questions related to the sine rule are combined with the cosine rule and or area of a triangle. Once students have learnt all 3 aspects then complete exam questions.
Next Steps
Cosine Rule and area of a triangle
Assessment
PLC/Reformed Specification/Target7/Geometry & Measures/Sine Rule

3. Key Vocabulary
Angle Side Re-arrange Sine or sin

4. Can be used in two situations
The Sine Rule
𝑎 𝑠𝑖𝑛𝐴 = 𝑏 𝑠𝑖𝑛𝐵
Lower case = sides
Capitals = angles
Can be used in two situations
Find missing length (if have 2 angles and 1 opposite side)
(2) Find missing Angle (if have 2 sides and 1 opposite angle)     
𝑠𝑖𝑛𝐴 𝑎 = 𝑠𝑖𝑛𝐵 𝑏
𝑎 𝑠𝑖𝑛𝐴 = 𝑏 𝑠𝑖𝑛𝐵   

5. Can you use the Sine Rule?X X    X X 
91º X  
46º X  X   X
11cm X

6. Can be used in two situations
The Sine Rule
𝑎 𝑠𝑖𝑛𝐴 = 𝑏 𝑠𝑖𝑛𝐵
Lower case = sides
Capitals = angles
Can be used in two situations
Find missing length (if have 2 angles and 1 opposite side)
(2) Find missing Angle (if have 2 sides and 1 opposite angle)        
Steps:
(1) Decide if you can use the Sine Rule
(2) Label the sides and angles with letters to work for the formula.
(3) Substitute them in to the formula, rearrange and solve

7. Example – Missing side Learn the formula:- 𝑎 𝑠𝑖𝑛𝐴 = 𝑏 𝑠𝑖𝑛𝐵
Find the length of ‘?’ 1dp.
Label sides
Substitute in values: 𝑠𝑖𝑛40 = 𝑏 𝑠𝑖𝑛45
Multiply the sin45 up to eliminate the divide.
4 𝑠𝑖𝑛45 𝑠𝑖𝑛40 =𝑏
4) Type in to calculator:4.4cm to 1dp
to 1dp
40o b ? B
45o
4cm a

8. Example – Missing Angle
𝑠𝑖𝑛𝐴 𝑎 = 𝑠𝑖𝑛𝐵 𝑏
Learn the formula:-
Find the angle ‘?’ 1dp.
Label sides
Substitute in values:
Multiply the 5 to the other side to eliminate the divide
sinA= 5𝑠𝑖𝑛48 6
3) Inverse sin (ie sin-1) your answer:
A=38.3o to 1 dp. A
6cm
5cm ?o
48o b
𝑠𝑖𝑛𝐴 5 = 𝑠𝑖𝑛48 6 a

9. Practice 1
Find the side length OR angle of each of the following triangles to 1 decimal place.
𝑠𝑖𝑛100 5 = 𝑠𝑖𝑛? 3.5
3.5𝑠𝑖𝑛100 5 =𝑠𝑖𝑛?
?=43.6o to 1dp
100o
3.5cm ?o
5 𝑠𝑖𝑛65 = ? 𝑠𝑖𝑛85
5𝑠𝑖𝑛85 𝑠𝑖𝑛65 =?
?=5.5cm to 1dp
65o
5cm
8cm ?
85o
5cm
17cm
19cm
35o
19 𝑠𝑖𝑛87 = ? 𝑠𝑖𝑛35
19𝑠𝑖𝑛35 𝑠𝑖𝑛87 =?
?=10.9cm to 1dp
87o ?

10. Practice 2 7.6 𝑠𝑖𝑛91 = ? 𝑠𝑖𝑛46 7.6𝑠𝑖𝑛46 𝑠𝑖𝑛91 =? ?=5.5cm to 1dp
91º X
46º
𝑠𝑖𝑛73 11 = 𝑠𝑖𝑛? 10
10𝑠𝑖𝑛73 11 =𝑠𝑖𝑛?
?=60.4o to 1dp X
11cm

11. Problem Solving and Reasoning
A triangular garden has the measurements shown on the diagram – what length of fence is needed to go all of the way around?
18m
52.4o
55.6o
72o
15m
𝑠𝑖𝑛72 18 = 𝑠𝑖𝑛? 15 , 𝑠𝑜 15𝑠𝑖𝑛72 18 =𝑠𝑖𝑛?
?=52.4o and the other missing angle will be 55.6o.
15 𝑠𝑖𝑛52.4 = ? 𝑠𝑖𝑛55.6 , 𝑠𝑜 15𝑠𝑖𝑛55.6 𝑠𝑖𝑛52.4 =?
The missing side is 15.6.
The perimeter is =48.6 metres.

12. Can be used in two situations
The Sine Rule
𝑎 𝑠𝑖𝑛𝐴 = 𝑏 𝑠𝑖𝑛𝐵
Lower case = sides
Capitals = angles
Can be used in two situations
Find missing length (if have 2 angles and 1 opposite side)
(2) Find missing Angle (if have 2 sides and 1 opposite angle)
Steps:
(1)
(2)
(3)
Student Sheet 1

13. Can you use the Sine Rule?X X X X
91º X
46º X X X
11cm X
Student Sheet 2

14. Examples
Student Sheet 3

15. Practice 1
Find the side length OR angle of each of the following triangles to 1 decimal place.
100o
3.5cm ?o
65o
5cm
8cm ?
85o
5cm
17cm
19cm
35o
87o ?
Student Sheet 4

16. Practice 2
91º X
46º X
11cm
Student Sheet 5

17. Problem Solving and Reasoning
A triangular garden has the measurements shown on the diagram – what length of fence is needed to go all of the way around?
18m
72o
15m
Student Sheet 5