1. Front Slide
Jo Richardson Community School

2. Jo Richardson Community School BTEC First Diploma in Engineering
Using Arithmetic
Solve the following two problems using the appropriate arithmetic to ensure that your answers are realistic and reasonable
Problem 1:
You are manufacturing a series of tools in a batch. The batch consists of 13 parts. You must manufacture the parts
using a length of cold rolled steel at 40x20x400. Each part to be manufactured has an overall size of 40x20x40.
1. Calculate how many parts can be made from the length of steel.
Problem 2:
Each part that you manufacture must have a section from it removed. This section is located in the centre of each
part and is sized at 15mm2
1. Calculate how much waste there will be per square as a percentage to the manufactured part.
2. Calculate the overall waste from the entire length of steel.
Name: Candidate No:
Unit 3: Mathematics for Engineering Technicians Task: 1a(i,ii) Grading Criteria: P Key Skills:
Assignment 1: Using arithmetic to solve engineering problems
Jo Richardson Community School
BTEC First Diploma in Engineering

3. Jo Richardson Community School BTEC First Diploma in Engineering
Plotting Graphs
Linear graphs
From these results create a graph showing the relationship between those two quantities (plot I(mA) on the X-axis). V 1 2 3 4 5
I (mA) 10 20 30 40 50 y x
Name: Candidate No:
Unit 3: Mathematics for Engineering Technicians Task: 1b(i) Grading Criteria: P Key Skills:
Assignment 1: Plotting linear graphs
Jo Richardson Community School
BTEC First Diploma in Engineering

4. Jo Richardson Community School BTEC First Diploma in Engineering
Plotting Graphs
Linear graphs
From these results create a graph showing the relationship between those two quantities (plot I(mA) on the X-axis). V 1 2 3 4 5
I (mA) 10 20 30 40 50
Name: Candidate No:
Unit 3: Mathematics for Engineering Technicians Task: 1b(i) Grading Criteria: P3 Key Skills:
Assignment 1: Plotting linear graphs T
Jo Richardson Community School
BTEC First Diploma in Engineering

5. Jo Richardson Community School BTEC First Diploma in Engineering
Plotting Graphs
Non-linear graphs
A light bulb has been tested for its electrical properties and the results collected are shown in the table below:
From these results create a graph showing the relationship between those two quantities (plot I(mA) on the X-axis). V 1 2 3 4 5
I (mA) 19 31 39 47 53 y x
Name: Candidate No:
Unit 3: Mathematics for Engineering Technicians Task: 1b(ii) Grading Criteria: P Key Skills:
Assignment 1: Plotting non-linear graphs
Jo Richardson Community School
BTEC First Diploma in Engineering

6. Jo Richardson Community School BTEC First Diploma in Engineering
Plotting Graphs
Non-linear graphs
A light bulb has been tested for its electrical properties and the results collected are shown in the table below:
From these results create a graph showing the relationship between those two quantities (plot I(mA) on the X-axis). V 1 2 3 4 5
I (mA) 19 31 39 47 53
Name: Candidate No:
Unit 3: Mathematics for Engineering Technicians Task: 1b(ii) Grading Criteria: P Key Skills:
Assignment 1: Plotting non-linear graphs T
Jo Richardson Community School
BTEC First Diploma in Engineering

7. Jo Richardson Community School BTEC First Diploma in Engineering
Transposition and Evaluation of Formulae
Use mathematical methods to transpose and evaluate simple formulae
Simplify these expressions, removing brackets where possible, and write your result in algebraic form: a) b)
A temperature F, measured on the Fahrenheit scale, and the same temperature C, on the Celsius scale, are
related by the formula:
2. Convert the following temperatures to the Fahrenheit scale.
a) Normal body temperature: 37oC
b) Room temperature: 20oC
B Brackets
O Order (Powers)
D Division
M Multiplication
A Addition
S Subtraction
Name: Candidate No:
Unit 3: Mathematics for Engineering Technicians Task: 2a Grading Criteria: P Key Skills:
Assignment 2: Use mathematical methods to transpose and evaluate simple formulae
Jo Richardson Community School
BTEC First Diploma in Engineering

8. Jo Richardson Community School BTEC First Diploma in Engineering
Transposition and Evaluation of Formulae
Use mathematical methods to transpose and evaluate simple formulae
Simplify these expressions, removing brackets where possible, and write your result in algebraic form: a) b)
A temperature F, measured on the Fahrenheit scale, and the same temperature C, on the Celsius scale, are
related by the formula:
2. Convert the following temperatures to the Fahrenheit scale.
a) Normal body temperature: 37oC
b) Room temperature: 20oC
6 – (4 x 2) 6 – 8 = -2
(2) 2a 2 x 2a = 4a
B Brackets
O Order (Powers)
D Division
M Multiplication
A Addition
S Subtraction
F = 9 x (37) + 32 F = 98.6 5
F = 9 x (20) + 32 F = 68 5
Name: Candidate No:
Unit 3: Mathematics for Engineering Technicians Task: 2a Grading Criteria: P Key Skills:
Assignment 1: Use mathematical methods to transpose and evaluate simple formulae T
Jo Richardson Community School
BTEC First Diploma in Engineering

9. Jo Richardson Community School BTEC First Diploma in Engineering
Transposition and Evaluation of Formulae
Transpose and evaluate a complex formula
You must correctly answer the following showing your workings
The general equation for a straight line is:
Transpose the formula to make x the subject of the formula
Evaluate x when m = 8.5, y = 120 and c = 75.
Name: Candidate No:
Unit 3: Mathematics for Engineering Technicians Task: 2b(i) Grading Criteria: M Key Skills:
Assignment 2: Transposition and evaluation of formula
Jo Richardson Community School
BTEC First Diploma in Engineering

10. Jo Richardson Community School BTEC First Diploma in Engineering
Transposition and Evaluation of Formulae
Transpose and evaluate a complex formula
You must correctly answer the following showing your workings
The general equation for a straight line is:
Transpose the formula to make x the subject of the formula
Evaluate x when m = 8.5, y = 120 and c = 75.
y = m x + c y – c = m x y - c = x x = y – c m m
x = y – c
x = (120-75)
x = 4 5
x = to 3d.p m
8.5
8.5
Name: Candidate No:
Unit 3: Mathematics for Engineering Technicians Task: 2b(i) Grading Criteria: M Key Skills:
Assignment 2: Transposition and evaluation of formula T
Jo Richardson Community School
BTEC First Diploma in Engineering

11. Jo Richardson Community School BTEC First Diploma in Engineering
Transposition and Evaluation of Formulae
Transpose and evaluate a complex formula
You must correctly answer the following showing your workings
Using the following common equation,
Transpose the formula to make u the subject of the formula.
Evaluate u when t = 20, a = 0.5 and s = 200.
Name: Candidate No:
Unit 3: Mathematics for Engineering Technicians Task: 2b(ii) Grading Criteria: M Key Skills:
Assignment 2: Transposition and evaluation of formula
Jo Richardson Community School
BTEC First Diploma in Engineering

12. Jo Richardson Community School BTEC First Diploma in Engineering
Transposition and Evaluation of Formulae
Transpose and evaluate a complex formula
You must correctly answer the following showing your workings
Using the following common equation,
Transpose the formula to make u the subject of the formula.
Evaluate u when t = 20, a = 0.5 and s = 200.
s = u t + ½ a t2 s - ½ a t2 = u t s – ½ a t2 = u s – 1(a t2) = u s – (a t2) = u
s – a t = u u = ½ (s – a t) t 2t 2t t
u = ½ (s – a t)
u = ½ (200 – 0.5 x 20)
u = ½ (200 – 10)
u = ½ x 190
u = 95
Name: Candidate No:
Unit 3: Mathematics for Engineering Technicians Task: 2b(ii) Grading Criteria: M Key Skills:
Assignment 2: Transposition and evaluation of formula T
Jo Richardson Community School
BTEC First Diploma in Engineering

13. Jo Richardson Community School BTEC First Diploma in Engineering
Transposition and Evaluation of Formulae
Transpose and evaluate a complex formula
You must correctly answer the following showing your workings
Using the following common equation,
Transpose the formula to make c the subject of the formula.
Evaluate c when a = 1.75 and b = 0.25
Name: Candidate No:
Unit 3: Mathematics for Engineering Technicians Task: 2b(iii) Grading Criteria: M Key Skills:
Assignment 2: Transposition and evaluation of formula
Jo Richardson Community School
BTEC First Diploma in Engineering

14. Jo Richardson Community School BTEC First Diploma in Engineering
Transposition and Evaluation of Formulae
Transpose and evaluate a complex formula
You must correctly answer the following showing your workings
Using the following common equation,
Transpose the formula to make c the subject of the formula.
Evaluate c when a = 1.75 and b = 0.25
b2 = (a2 – c2) b2 + c2 = a2 a2 – b2 = c2 c = (a2 – b2) 
c = (a2 – b2) c = (1.752 – 0.252) c = ( – ) c = 3   
Name: Candidate No:
Unit 3: Mathematics for Engineering Technicians Task: 2b(iii) Grading Criteria: M Key Skills:
Assignment 2: Transposition and evaluation of formula T
Jo Richardson Community School
BTEC First Diploma in Engineering

15. Jo Richardson Community School BTEC First Diploma in Engineering
Transposition and Evaluation of Formulae
Transpose and evaluate combining formulae
You must correctly answer the following showing your workings
Using the following common equation,
I2R = VI
Transpose the formula to make V the subject of the formula.
Evaluate V when I = 4 and R = 1
Name: Candidate No:
Unit 3: Mathematics for Engineering Technicians Task: 2c Grading Criteria: D Key Skills:
Assignment 2: Transposition and evaluation of formula
Jo Richardson Community School
BTEC First Diploma in Engineering

16. Jo Richardson Community School BTEC First Diploma in Engineering
Transposition and Evaluation of Formulae
Transpose and evaluate combining formulae
You must correctly answer the following showing your workings
Using the following common equation,
I2R = VI
Transpose the formula to make V the subject of the formula.
I2 R = V I I2 R = V I2 R = V I R = V V = I R
Evaluate V when I = 4 and R = 1
V = I R
V = 4 x 1
V = 4 I I
Name: Candidate No:
Unit 3: Mathematics for Engineering Technicians Task: 2c Grading Criteria: D Key Skills:
Assignment 2: Transposition and evaluation of formula T
Jo Richardson Community School
BTEC First Diploma in Engineering

17. Jo Richardson Community School BTEC First Diploma in Engineering
Using a Scientific Calculator
Perform chained calculations in assignment 2 using the basic and special functions keys of an electronic scientific calculator.
Using the buttons adjacent, show the steps you have
taken to complete Task 2bi
Name: Candidate No:
Unit 3: Mathematics for Engineering Technicians Task: 2d Grading Criteria: D Key Skills:
Assignment 2: Using a Scientific Calculator
Jo Richardson Community School
BTEC First Diploma in Engineering

18. Jo Richardson Community School BTEC First Diploma in Engineering
Using a Scientific Calculator
Carry out chained calculations using an electronic calculator. You will be observed during these tasks.
YOU MUST MAKE SURE YOU GET YOUR OBSERVATION SHEET SIGNED TO ACHIEVE THIS
GRADE CRITERIA.
Name: Candidate No:
Unit 3: Mathematics for Engineering Technicians Task: 2d Grading Criteria: D Key Skills:
Assignment 2: Using a Scientific Calculator
Jo Richardson Community School
BTEC First Diploma in Engineering

19. Jo Richardson Community School BTEC First Diploma in Engineering
Surface area of regular shapes
Calculate the surface area for TWO shapes. These shapes are similar to those used in your practical sessions. The
data can be used to determine the amount of finishing needed to complete the projects by polishing the faces and
the quantity of materials used.
Scribing Block
Depth Gauge
40mm
30mm
25mm
25mm
40mm
Name: Candidate No:
Unit 3: Mathematics for Engineering Technicians Task: 3a Grading Criteria: P Key Skills:
Assignment 3: Calculating surface area of regular shapes
Jo Richardson Community School
BTEC First Diploma in Engineering

20. Jo Richardson Community School BTEC First Diploma in Engineering
Surface area of regular shapes
Calculate the surface area for TWO shapes. These shapes are similar to those used in your practical sessions. The
data can be used to determine the amount of finishing needed to complete the projects by polishing the faces and
the quantity of materials used.
Scribing Block
Depth Gauge
Known:
Side A x 2
Side B x 2
Side C x 2
Surface Area of A
25mm x 40mm = 1000mm2
Surface Area of B
40mm x 30mm = 1200mm2
Surface Area of C
30mm x 25mm = 750mm2
Total Surface Area = 2(SAA) + 2(SAB) + 2(SAC)
= 2(1000) + 2(1200) + 2(750) =
= 5900mm2
40mm
30mm
25mm B C A
Surface Area of A
A =  r2 A =  x (1/2d) A =  x (1/2 x 25)2
A =  x A = mm2 2d.p
Surface Area of B
A = C x height A = (d) x height
A = (78.540) x 40
A = mm2 2d.p
Total Surface Area = 2(SAA) + SAB
= (2 x ) =
= mm2
Known:
C = 2r or C = d
A =  r2
d = 2r or r = ½ d
Side A x 2
Side B x 1
25mm A
40mm B B
Name: Candidate No:
Unit 3: Mathematics for Engineering Technicians Task: 3a Grading Criteria: P Key Skills:
Assignment 3: Calculating surface area of regular shapes T
Jo Richardson Community School
BTEC First Diploma in Engineering

21. Jo Richardson Community School BTEC First Diploma in Engineering
Volume of regular shapes
Calculate the volume for TWO shapes. These shapes are similar to those used in your practical sessions. The
data can be used to determine the amount of finishing needed to complete the projects by polishing the faces and
the quantity of materials used.
Scribing Block
Depth Gauge
40mm
30mm
25mm
25mm
40mm
Name: Candidate No:
Unit 3: Mathematics for Engineering Technicians Task: 3b Grading Criteria: P Key Skills:
Assignment 3: Calculating volume of regular shapes
Jo Richardson Community School
BTEC First Diploma in Engineering

22. Jo Richardson Community School BTEC First Diploma in Engineering
Volume of regular shapes
Calculate the volume for TWO shapes. These shapes are similar to those used in your practical sessions. The
data can be used to determine the amount of finishing needed to complete the projects by polishing the faces and
the quantity of materials used.
Scribing Block
Depth Gauge
Known:
Cross Section = A
V = A x length
Surface Area of A
25mm x 40mm = 1000mm2
Volume of Shape
V = 1000 x 30
V = 30000mm3
40mm
30mm
25mm B C A
Known:
Cross Section = A
A =  r2
d = 2r or r = ½ d
V = A x length
Surface Area of A
A =  r2 A =  x (1/2d) A =  x (1/2 x 25)2
A =  x A = mm2 2d.p
Volume of Shape
V = x 40
V = mm3
25mm A
40mm B
Name: Candidate No:
Unit 3: Mathematics for Engineering Technicians Task: 3b Grading Criteria: P Key Skills:
Assignment 3: Calculating volume of regular shapes T
Jo Richardson Community School
BTEC First Diploma in Engineering

23. Jo Richardson Community School BTEC First Diploma in Engineering
Surface area of compound shapes
You must ‘identify’ the ‘data’ required and determine (calculate) the TOTAL SURFACE AREA of TWO compound
shapes – you must show ALL your workings
SHAPE 1 – Trapezoid 40 A B
130 50 60 CL
Name: Candidate No:
Unit 3: Mathematics for Engineering Technicians Task: 3c(i) Grading Criteria: M Key Skills:
Assignment 3: identify the data required and determine the area of two compound shapes
Jo Richardson Community School
BTEC First Diploma in Engineering

24. Jo Richardson Community School BTEC First Diploma in Engineering
Surface area of compound shapes
You must ‘identify’ the ‘data’ required and determine (calculate) the TOTAL SURFACE AREA of TWO compound
shapes – you must show ALL your workings
SHAPE 1 – Trapezoid
Known:
Side A x 2
Side B x 2
Top x 1
Base x 1
Total Surface Area of A = i + ii + iii
i = ½ (1/2(130-40) x 60)
i = ½ (2700)
i = 1350
i = iii therefore iii = 1350
ii = 40 x 60
ii = 2400 =
= 5100
Surface Area of B
Find x using Pythagoras Theorem c = x
c2 = a2 + b2
c =  a2 + b2
c = 
c = 5625
c = 75 therefore x = 75
Total Area = 75 x 50
Total Area = 3750
Surface Area of Top
Area = 40 x 50 = 2000
Surface Area of Base
Area = 130 x 50 = 65000
Total Surface Area = 2A + 2B + Top + Base
= 2(5100) + 2(3750) =
= 84700 40 A B
130 50 x 60 x b i ii
iii CL a
Name: Candidate No:
Unit 3: Mathematics for Engineering Technicians Task: 3c(i) Grading Criteria: M Key Skills:
Assignment 3: identify the data required and determine the area of two compound shapes T
Jo Richardson Community School
BTEC First Diploma in Engineering

25. Jo Richardson Community School BTEC First Diploma in Engineering
Surface area of compound shapes
You must ‘identify’ the ‘data’ required and determine (calculate) the TOTAL SURFACE AREA of TWO compound
shapes – you must show ALL your workings
Scribing Block Base 50 80
160
R = 40
Name: Candidate No:
Unit 3: Mathematics for Engineering Technicians Task: 3c(ii) Grading Criteria: M Key Skills:
Assignment 3: identify the data required and determine the area of two compound shapes
Jo Richardson Community School
BTEC First Diploma in Engineering

26. Jo Richardson Community School BTEC First Diploma in Engineering
Surface area of compound shapes
You must ‘identify’ the ‘data’ required and determine (calculate) the TOTAL SURFACE AREA of TWO compound
shapes – you must show ALL your workings
Scribing Block Base
Known:
Side A x 2
Side B x 2
Side C x 1
Side D x 1
Total Surface Area of A = A + Ai
A = 80 x 80 = 6400
To find Ai, find the ½ the area or a circle when r = 40
Area = r2
Area =  x 1600
Area =
Therefore total area = A + Ai = =
Surface Area of B
Area = 80 x 50 = 4000
Surface Area of C
Surface Area of D
To find curve – find the circumference of the ½ circle when r = 40
Circumference = 2r
Circumference = 2 x  x 40
Circumference =
½ Circumference =
Area = x 50
= 6283
Total Surface Area
Area = 2A + 2B + C + D
= 2( ) + 2(4000) = = 50 B 80 C A D D Ai
160
R = 40 80 CL
Name: Candidate No:
Unit 3: Mathematics for Engineering Technicians Task: 3c(ii) Grading Criteria: M Key Skills:
Assignment 3: identify the data required and determine the area of two compound shapes T
Jo Richardson Community School
BTEC First Diploma in Engineering

27. Jo Richardson Community School BTEC First Diploma in Engineering
Surface area of compound shapes
You must ‘identify’ the ‘data’ required and determine (calculate) the TOTAL VOLUME of TWO compound
shapes – you must show ALL your workings
SHAPE 1 – Trapezoid 40 A B
130 50 60 CL
Name: Candidate No:
Unit 3: Mathematics for Engineering Technicians Task: 3d(i) Grading Criteria: M Key Skills:
Assignment 3: identify the data required and determine the volume of two compound shapes
Jo Richardson Community School
BTEC First Diploma in Engineering

28. Jo Richardson Community School BTEC First Diploma in Engineering
Surface area of compound shapes
You must ‘identify’ the ‘data’ required and determine (calculate) the TOTAL VOLUME of TWO compound
shapes – you must show ALL your workings
SHAPE 1 – Trapezoid
Total Surface Area of A = 5100
Volume = Surface Area x length
= 5100 x 50 = 40 A B
130 50 60 CL
Name: Candidate No:
Unit 3: Mathematics for Engineering Technicians Task: 3d(i) Grading Criteria: M Key Skills:
Assignment 3: identify the data required and determine the volume of two compound shapes T
Jo Richardson Community School
BTEC First Diploma in Engineering

29. Jo Richardson Community School BTEC First Diploma in Engineering
Surface area of compound shapes
You must ‘identify’ the ‘data’ required and determine (calculate) the TOTAL VOLUME of TWO compound
shapes – you must show ALL your workings
Scribing Block Base – 50 80 A Ai
160
R = 40
Name: Candidate No:
Unit 3: Mathematics for Engineering Technicians Task: 3d(ii) Grading Criteria: M Key Skills:
Assignment 3: identify the data required and determine the area of two compound shapes
Jo Richardson Community School
BTEC First Diploma in Engineering

30. Jo Richardson Community School BTEC First Diploma in Engineering
Surface area of compound shapes
You must ‘identify’ the ‘data’ required and determine (calculate) the TOTAL VOLUME of TWO compound
shapes – you must show ALL your workings
Scribing Block Base –
Total Surface Area of A = A + Ai
= A + Ai = =
Volume = Surface Area x length
= x 50 = 50 80 A Ai
160
R = 40
Name: Candidate No:
Unit 3: Mathematics for Engineering Technicians Task: 3d(ii) Grading Criteria: M Key Skills:
Assignment 3: identify the data required and determine the area of two compound shapes T
Jo Richardson Community School
BTEC First Diploma in Engineering

31. Jo Richardson Community School BTEC First Diploma in Engineering
Using Pythagoras
Pythagoras’ Theorem to find the hypotenuse, opposite and tangent length
Using Pythagoras’s theorem, calculate the length of the hypotenuse, giving your results in metres. Show all steps in your calculations. B
20mm
a2 + b2 = c2 A C
30mm
Likewise
c2 - a2 = b2 c a
c2 - b2 = a2
Hypotenuse
Opposite b
Adjacent
Name: Candidate No:
Unit 3: Mathematics for Engineering Technicians Task: 4a(i) Grading Criteria: P Key Skills:
Assignment 4: Solutions to right angle triangle problems
Jo Richardson Community School
BTEC First Diploma in Engineering

32. Jo Richardson Community School BTEC First Diploma in Engineering
Using Pythagoras
Pythagoras’ Theorem to find the hypotenuse, opposite and tangent length
Using Pythagoras’s theorem, calculate the length of the hypotenuse, giving your results in metres. Show all steps in your calculations. B
C =  a2 + b2
C = 
C =  ( )
C =  1300
C = 36.06mm
20mm
a2 + b2 = c2 A C
30mm
Likewise
c2 - a2 = b2 c a
c2 - b2 = a2
Hypotenuse
Opposite b
Adjacent
Name: Candidate No:
Unit 3: Mathematics for Engineering Technicians Task: 4a(i) Grading Criteria: P Key Skills:
Assignment 4: Solutions to right angle triangle problems T
Jo Richardson Community School
BTEC First Diploma in Engineering

33. Jo Richardson Community School BTEC First Diploma in Engineering
Using Pythagoras
Pythagoras’ Theorem to find the hypotenuse, opposite and tangent length
Using Pythagoras’s theorem, calculate the length of the hypotenuse, giving your results in metres. Show all steps in your calculations.
100cm
85cm X
a2 + b2 = c2
80m
20m X
Likewise
c2 - a2 = b2 c a
c2 - b2 = a2 X
80cm b
120cm
Name: Candidate No:
Unit 3: Mathematics for Engineering Technicians Task: 4a(ii) Grading Criteria: P Key Skills:
Assignment 4: Solutions to right angle triangle problems
Jo Richardson Community School
BTEC First Diploma in Engineering

34. Jo Richardson Community School BTEC First Diploma in Engineering
Using Pythagoras
Pythagoras’ Theorem to find the hypotenuse, opposite and tangent length
Using Pythagoras’s theorem, calculate the length of the hypotenuse, giving your results in metres. Show all steps in your calculations.
X =  a2 + b2
C = 
C =  ( )
C =  17225
C = cm
100cm
85cm X
X =  a2 + b2
C = 
C =  ( )
C =  6800
C = 82.46m
a2 + b2 = c2
80m
20m X
Likewise
c2 - a2 = b2 c a
c2 - b2 = a2
X =  c2 - a2
C = 
C =  ( )
C =  8000
C = 89.44cm X
80cm b
120cm
Name: Candidate No:
Unit 3: Mathematics for Engineering Technicians Task: 4a(ii) Grading Criteria: P Key Skills:
Assignment 4: Solutions to right angle triangle problems T
Jo Richardson Community School
BTEC First Diploma in Engineering

35. Jo Richardson Community School BTEC First Diploma in Engineering
Sine, Cosine and Tangent ratio tables
Name: Candidate No:
Unit 3: Mathematics for Engineering Technicians Task: Grading Criteria: FACT SHEET Key Skills:
Assignment 4: Sine, Cosine and Tangent ratio tables FACT SHEET
Jo Richardson Community School
BTEC First Diploma in Engineering

36. Jo Richardson Community School BTEC First Diploma in Engineering
There are three formulae involved in trigonometry
Sine = opposite/hypotenuse
Cosine = adjacent/hypotenuse
Tangent = opposite/adjacent
These can easily be remembered using SOH CAH TOA
Using Pythagoras
Pythagoras’ Theorem using sine, cosine and tangent ratios
Using sine, cosine and tangent tables, calculate the following: 1. 3. a
20cm
650 2.
15mm a
Name: Candidate No:
Unit 3: Mathematics for Engineering Technicians Task: 4b Grading Criteria: P6 Key Skills:
Assignment 4: Solutions to right angle triangle problems T
Jo Richardson Community School
BTEC First Diploma in Engineering

37. Jo Richardson Community School BTEC First Diploma in Engineering
There are three formulae involved in trigonometry
Sine = opposite/hypotenuse
Cosine = adjacent/hypotenuse
Tangent = opposite/adjacent
These can easily be remembered using SOH CAH TOA
Using Pythagoras
Pythagoras’ Theorem using sine, cosine and tangent ratios
Using sine, cosine and tangent tables, calculate the following:
Using the Tangent Ratio Table
Known – adjacent and opposite values
Tan (angle) = opposite / adjacent
Tan 28 = a / 15
a = tan 28 x 15
a = x 15
a = 7.98mm 1. 3. a
20cm
650
Using the Cosine Ratio Table
Known – adjacent and hypotenuse values
Cos (angle) = adjacent / hypotenuse
Cos 65 = a / 20
a = cos 65 x 20
a = x 20
a = 8.45cm 2.
Using the Sine Ratio Table
Known – opposite and hypotenuse values
Sin (angle) = opposite / hypotenuse
Sin 25 = 15 / a
Sin25 x a = 15
a = 15 / sin25
a = 15 /
a = 35.49m
15mm a
Name: Candidate No:
Unit 3: Mathematics for Engineering Technicians Task: 4b Grading Criteria: P Key Skills:
Assignment 4: Solutions to right angle triangle problems T
Jo Richardson Community School
BTEC First Diploma in Engineering

38. Jo Richardson Community School BTEC First Diploma in Engineering
Using trigonometry to solve complex shapes
Calculate the length of VA
Name: Candidate No:
Unit 3: Mathematics for Engineering Technicians Task: 4c Grading Criteria: M Key Skills:
Assignment 4: Using trigonometry to solve complex shapes
Jo Richardson Community School
BTEC First Diploma in Engineering

39. Jo Richardson Community School BTEC First Diploma in Engineering
Using trigonometry to solve complex shapes
Calculate the length of VA
Name: Candidate No:
Unit 3: Mathematics for Engineering Technicians Task: 4c Grading Criteria: M Key Skills:
Assignment 4: Using trigonometry to solve complex shapes T
Jo Richardson Community School
BTEC First Diploma in Engineering