Edexcel Level 2
BTEC First Diploma in Engineering
Unit 3
Mathematics for Engineering
Technicians
Academic Year:
Jo Richardson Community School
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:
Jo Richardson Community School
BTEC First Diploma in Engineering
Candidate No:
Unit 3: Mathematics for Engineering Technicians
Assignment 1: Using arithmetic to solve engineering problems
Task: 1a(i,ii)
Grading Criteria: P1
Key Skills:
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
0
I (mA)
0
1
10
2
3
4
5
20
30
40
50
y
x
Name:
Jo Richardson Community School
BTEC First Diploma in Engineering
Candidate No:
Unit 3: Mathematics for Engineering Technicians
Assignment 1: Plotting linear graphs
Task: 1b(i)
Grading Criteria: P3
Key Skills:
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
0
I (mA)
0
1
10
2
3
4
5
20
30
40
50
Voltage (V)
Relationship between Current and
Voltage
60
50
40
30
20
10
0
0
1
2
3
4
5
6
Current (I(mA))
Name:
Jo Richardson Community School
BTEC First Diploma in Engineering
Candidate No:
Unit 3: Mathematics for Engineering Technicians
Assignment 1: Plotting linear graphs
Task: 1b(i)
Grading Criteria: P3
Key Skills:
T
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
0
I (mA)
0
1
19
2
31
3
4
5
39
47
53
y
x
Name:
Jo Richardson Community School
BTEC First Diploma in Engineering
Candidate No:
Unit 3: Mathematics for Engineering Technicians
Assignment 1: Plotting non-linear graphs
Task: 1b(ii)
Grading Criteria: P3
Key Skills:
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
0
I (mA)
0
1
19
2
31
3
4
5
39
47
53
Voltage (V)
Relationship between Current and
Voltage
60
50
40
30
20
10
0
0
1
2
3
4
5
6
Current (I(mA))
Name:
Jo Richardson Community School
BTEC First Diploma in Engineering
Candidate No:
Unit 3: Mathematics for Engineering Technicians
Assignment 1: Plotting non-linear graphs
Task: 1b(ii)
Grading Criteria: P3
Key Skills:
T
Transposition and Evaluation of Formulae
Use mathematical methods to transpose and evaluate simple formulae
1.
Simplify these expressions, removing brackets where possible, and write your result in algebraic form:
a)
6  4 2
b)
6  42a
A temperature F, measured on the Fahrenheit scale, and the same temperature C, on the Celsius scale, are
related by the formula:
F
9
C  32
5
2.
Convert the following temperatures to the Fahrenheit scale.
a)
Normal body temperature: 37oC
b)
Room temperature: 20oC
Name:
Jo Richardson Community School
BTEC First Diploma in Engineering
B
Brackets
O
Order (Powers)
D
Division
M
Multiplication
A
Addition
S
Subtraction
Candidate No:
Unit 3: Mathematics for Engineering Technicians
Task: 2a
Grading Criteria: P2
Assignment 2: Use mathematical methods to transpose and evaluate simple formulae
Key Skills:
Transposition and Evaluation of Formulae
Use mathematical methods to transpose and evaluate simple formulae
1.
Simplify these expressions, removing brackets where possible, and write your result in algebraic form:
a)
6  4 2
6 – (4 x 2)
6–8
= -2
b)
6  42a
(2) 2a
2 x 2a
= 4a
A temperature F, measured on the Fahrenheit scale, and the same temperature C, on the Celsius scale, are
related by the formula:
F
9
C  32
5
2.
Convert the following temperatures to the Fahrenheit scale.
a)
Normal body temperature: 37oC
b)
Room temperature: 20oC
Name:
Jo Richardson Community School
BTEC First Diploma in Engineering
F = 9 x (37) + 32
5
F = 9 x (20) + 32
5
F = 98.6
F = 68
B
Brackets
O
Order (Powers)
D
Division
M
Multiplication
A
Addition
S
Subtraction
Candidate No:
Unit 3: Mathematics for Engineering Technicians
Task: 2a
Grading Criteria: P2
Assignment 1: Use mathematical methods to transpose and evaluate simple formulae
Key Skills:
T
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:
y  mx  c
Transpose the formula to make x the subject of the formula
Evaluate x when m = 8.5, y = 120 and c = 75.
Name:
Jo Richardson Community School
BTEC First Diploma in Engineering
Candidate No:
Unit 3: Mathematics for Engineering Technicians
Assignment 2: Transposition and evaluation of formula
Task: 2b(i)
Grading Criteria: M1
Key Skills:
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:
y  mx  c
Transpose the formula to make x the subject of the formula
y–c=mx
y=mx+c
y-c=x
m
x=y–c
m
Evaluate x when m = 8.5, y = 120 and c = 75.
x=y–c
m
x = (120-75)
8.5
Name:
Jo Richardson Community School
BTEC First Diploma in Engineering
x= 45
8.5
x = 5.294 to 3d.p
Candidate No:
Unit 3: Mathematics for Engineering Technicians
Assignment 2: Transposition and evaluation of formula
Task: 2b(i)
Grading Criteria: M1
Key Skills:
T
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,
1
s  ut  at 2
2
Transpose the formula to make u the subject of the formula.
Evaluate u when t = 20, a = 0.5 and s = 200.
Name:
Jo Richardson Community School
BTEC First Diploma in Engineering
Candidate No:
Unit 3: Mathematics for Engineering Technicians
Assignment 2: Transposition and evaluation of formula
Task: 2b(ii)
Grading Criteria: M1
Key Skills:
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,
1
s  ut  at 2
2
Transpose the formula to make u the subject of the formula.
s = u t + ½ a t2
s - ½ a t2 = u t
s – ½ a t2 = u
t
s – 1(a t2) = u
2t
s – (a t2) = u
2t
s–at=u
u = ½ (s – a t)
t
Evaluate u when t = 20, a = 0.5 and s = 200.
u = ½ (s – a t)
u = ½ (200 – 0.5 x 20)
u = ½ (200 – 10)
u = ½ x 190
u = 95
Name:
Jo Richardson Community School
BTEC First Diploma in Engineering
Candidate No:
Unit 3: Mathematics for Engineering Technicians
Assignment 2: Transposition and evaluation of formula
Task: 2b(ii)
Grading Criteria: M1
Key Skills:
T
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,
b  (a 2  c 2 )
Transpose the formula to make c the subject of the formula.
Evaluate c when a = 1.75 and b = 0.25
Name:
Jo Richardson Community School
BTEC First Diploma in Engineering
Candidate No:
Unit 3: Mathematics for Engineering Technicians
Assignment 2: Transposition and evaluation of formula
Task: 2b(iii)
Grading Criteria: M1
Key Skills:
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,
b  (a 2  c 2 )
Transpose the formula to make c the subject of the formula.
b2 = (a2 – c2)
b2 + c2 = a2
a2 – b2 = c2
c = (a2 – b2)
c = (3.0625 – 0.0625)
c=3
Evaluate c when a = 1.75 and b = 0.25
c =  (a2 – b2)
c = (1.752 – 0.252)
Name:
Jo Richardson Community School
BTEC First Diploma in Engineering
Candidate No:
Unit 3: Mathematics for Engineering Technicians
Assignment 2: Transposition and evaluation of formula
Task: 2b(iii)
Grading Criteria: M1
Key Skills:
T
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:
Jo Richardson Community School
BTEC First Diploma in Engineering
Candidate No:
Unit 3: Mathematics for Engineering Technicians
Assignment 2: Transposition and evaluation of formula
Task: 2c
Grading Criteria: D1
Key Skills:
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
I
I2 R = V
I
IR=V
V=IR
Evaluate V when I = 4 and R = 1
V=IR
V=4x1
V=4
Name:
Jo Richardson Community School
BTEC First Diploma in Engineering
Candidate No:
Unit 3: Mathematics for Engineering Technicians
Assignment 2: Transposition and evaluation of formula
Task: 2c
Grading Criteria: D1
Key Skills:
T
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:
Jo Richardson Community School
BTEC First Diploma in Engineering
Candidate No:
Unit 3: Mathematics for Engineering Technicians
Assignment 2: Using a Scientific Calculator
Task: 2d
Grading Criteria: D2
Key Skills:
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:
Jo Richardson Community School
BTEC First Diploma in Engineering
Candidate No:
Unit 3: Mathematics for Engineering Technicians
Assignment 2: Using a Scientific Calculator
Task: 2d
Grading Criteria: D2
Key Skills:
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
40mm
25mm
30mm
Depth Gauge
25mm
40mm
Name:
Jo Richardson Community School
BTEC First Diploma in Engineering
Candidate No:
Unit 3: Mathematics for Engineering Technicians
Assignment 3: Calculating surface area of regular shapes
Task: 3a
Grading Criteria: P4
Key Skills:
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.
Known:
Surface Area of A
25mm x 40mm = 1000mm2
Side A x 2
Scribing Block
Side B x 2
40mm
Surface Area of B
40mm x 30mm = 1200mm2
Side C x 2
B
25mm
A
Surface Area of C
30mm x 25mm = 750mm2
C
Total Surface Area
= 2(SAA) + 2(SAB) + 2(SAC)
= 2(1000) + 2(1200) + 2(750)
= 2000 + 2400 + 1500
= 5900mm2
30mm
Depth Gauge
Surface Area of A
A =  r2
A =  x (1/2d)2
Known:
C = 2r or C = d
25mm
A =  r2
A
d = 2r
or r = ½ d
40mm
B
B
Side A x 2
A =  x 12.52
A = 490.87mm2 2d.p
Surface Area of B
A = C x height
A = (d) x height
A = (78.540) x 40
A = 3141.59mm2 2d.p
Total Surface Area
Side B x 1
Name:
Jo Richardson Community School
BTEC First Diploma in Engineering
A =  x (1/2 x 25)2
= 2(SAA) + SAB
= (2 x 490.87) + 3141.59
= 981.74 + 3141.59
= 4123.33mm2
Candidate No:
Unit 3: Mathematics for Engineering Technicians
Assignment 3: Calculating surface area of regular shapes
Task: 3a
Grading Criteria: P4
Key Skills:
T
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
40mm
25mm
30mm
Depth Gauge
25mm
40mm
Name:
Jo Richardson Community School
BTEC First Diploma in Engineering
Candidate No:
Unit 3: Mathematics for Engineering Technicians
Assignment 3: Calculating volume of regular shapes
Task: 3b
Grading Criteria: P5
Key Skills:
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.
Known:
Surface Area of A
Cross Section = A
Scribing Block
V = A x length
40mm
Volume of Shape
V = 1000 x 30
B
25mm
A
25mm x 40mm = 1000mm2
V = 30000mm3
C
30mm
Depth Gauge
Known:
25mm
A
Cross Section = A
Surface Area of A
A =  r2
A =  x (1/2d)2
A =  r2
A =  x 12.52 A = 490.87mm2 2d.p
d = 2r
40mm
A =  x (1/2 x 25)2
or r = ½ d
V = A x length
B
Volume of Shape
V = 490.87 x 40
V = 19634.8mm3
Name:
Jo Richardson Community School
BTEC First Diploma in Engineering
Candidate No:
Unit 3: Mathematics for Engineering Technicians
Assignment 3: Calculating volume of regular shapes
Task: 3b
Grading Criteria: P5
Key Skills:
T
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:
Jo Richardson Community School
BTEC First Diploma in Engineering
Candidate No:
Unit 3: Mathematics for Engineering Technicians
Task: 3c(i)
Grading Criteria: M2
Assignment 3: identify the data required and determine the area of two compound shapes
Key Skills:
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:
Total Surface Area of A
Side A x 2
i = ½ (1/2(130-40) x 60)
i = ½ (2700)
i = 1350
i = iii therefore iii = 1350
Side B x 2
40
Top x 1
Base x 1
ii = 40 x 60
ii = 2400
Total Surface Area of A
A
B
130
50
x
60
x
i
CL
Name:
Jo Richardson Community School
BTEC First Diploma in Engineering
ii
b
iii
a
= i + ii + iii
= i + ii + iii
= 1350 + 2400 + 1350
= 5100
Surface Area of B
Find x using Pythagoras Theorem
c=x
c2 = a2 + b2
c =  a2 + b2
c =  452 + 602
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) + 2000 + 65000
= 10200 + 7500 + 2000 + 65000
= 84700
Candidate No:
Unit 3: Mathematics for Engineering Technicians
Task: 3c(i)
Grading Criteria: M2
Assignment 3: identify the data required and determine the area of two compound shapes
Key Skills:
T
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:
Jo Richardson Community School
BTEC First Diploma in Engineering
Candidate No:
Unit 3: Mathematics for Engineering Technicians
Task: 3c(ii)
Grading Criteria: M2
Assignment 3: identify the data required and determine the area of two compound shapes
Key Skills:
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
Known:
Side A x 2
Scribing Block Base
Side B x 2
Side C x 1
50
Side D x 1
B
80
C
A
D
D
Ai
160
R = 40
80
CL
Name:
Jo Richardson Community School
BTEC First Diploma in Engineering
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 = 5026.55
Therefore total area
= A + Ai
= 6400 + 5026.55
= 11426.55
Surface Area of B
Area = 80 x 50 = 4000
Surface Area of C
Area = 80 x 50 = 4000
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
= 251.33
½ Circumference
= 125.66
Area
=125.66 x 50
= 6283
Total Surface Area
Area
= 2A + 2B + C + D
= 2(11426.55) + 2(4000) +4000 + 6283
= 22853.10 + 8000 + 4000 + 6283
= 41136.10
Candidate No:
Unit 3: Mathematics for Engineering Technicians
Task: 3c(ii)
Grading Criteria: M2
Assignment 3: identify the data required and determine the area of two compound shapes
Key Skills:
T
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:
Jo Richardson Community School
BTEC First Diploma in Engineering
Candidate No:
Unit 3: Mathematics for Engineering Technicians
Task: 3d(i)
Grading Criteria: M3
Assignment 3: identify the data required and determine the volume of two compound shapes
Key Skills:
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
Total Surface Area of A
= 5100
Volume
= Surface Area x length
= 5100 x 50
= 255000
SHAPE 1 – Trapezoid
40
A
B
130
50
60
CL
Name:
Jo Richardson Community School
BTEC First Diploma in Engineering
Candidate No:
Unit 3: Mathematics for Engineering Technicians
Task: 3d(i)
Grading Criteria: M3
Assignment 3: identify the data required and determine the volume of two compound shapes
Key Skills:
T
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:
Jo Richardson Community School
BTEC First Diploma in Engineering
Candidate No:
Unit 3: Mathematics for Engineering Technicians
Task: 3d(ii)
Grading Criteria: M3
Assignment 3: identify the data required and determine the area of two compound shapes
Key Skills:
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
= 6400 + 5026.55
= 11426.55
Volume
= Surface Area x length
= 11426.55 x 50
= 571327.5
50
80
A
Ai
160
R = 40
Name:
Jo Richardson Community School
BTEC First Diploma in Engineering
Candidate No:
Unit 3: Mathematics for Engineering Technicians
Task: 3d(ii)
Grading Criteria: M3
Assignment 3: identify the data required and determine the area of two compound shapes
Key Skills:
T
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  a b
2
2
20mm
a 2 + b2 = c 2
A
C
30mm
Likewise
c2
-
a2
=
c2 - b2 = a2
Opposite
c
b2
a
b
Adjacent
Name:
Jo Richardson Community School
BTEC First Diploma in Engineering
Candidate No:
Unit 3: Mathematics for Engineering Technicians
Assignment 4: Solutions to right angle triangle problems
Task: 4a(i)
Grading Criteria: P6
Key Skills:
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.
C =  a2 + b2
B
C =  202 + 302
C =  (400 + 900)
C =  1300
c  a b
2
2
C = 36.06mm
20mm
a 2 + b2 = c 2
A
C
30mm
Likewise
c2
-
a2
=
c2 - b2 = a2
Opposite
c
b2
a
b
Adjacent
Name:
Jo Richardson Community School
BTEC First Diploma in Engineering
Candidate No:
Unit 3: Mathematics for Engineering Technicians
Assignment 4: Solutions to right angle triangle problems
Task: 4a(i)
Grading Criteria: P6
Key Skills:
T
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
c  a b
2
85cm
2
100cm
a 2 + b2 = c 2
X
20m
Likewise
c2
80m
-
a2
=
c
b2
c2 - b2 = a2
a
X
120cm
Name:
Jo Richardson Community School
BTEC First Diploma in Engineering
b
80cm
Candidate No:
Unit 3: Mathematics for Engineering Technicians
Assignment 4: Solutions to right angle triangle problems
Task: 4a(ii)
Grading Criteria: P6
Key Skills:
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 =  852 + 1002
X
c  a b
85cm
C =  (7225 + 10000)
2
C =  17225
C = 131.24cm
100cm
X =  a2 + b2
C=
X
20m
80m
202
+
2
a 2 + b2 = c 2
802
C =  (400 + 6400)
C =  6800
Likewise
C = 82.46m
c2
-
a2
=
c
b2
c2 - b2 = a2
a
X
X =  c2 - a2
C =  1202 - 802
C =  (14400 - 6400)
120cm
C =  8000
b
80cm
C = 89.44cm
Name:
Jo Richardson Community School
BTEC First Diploma in Engineering
Candidate No:
Unit 3: Mathematics for Engineering Technicians
Assignment 4: Solutions to right angle triangle problems
Task: 4a(ii)
Grading Criteria: P6
Key Skills:
T
Sine, Cosine and Tangent ratio tables
Name:
Jo Richardson Community School
BTEC First Diploma in Engineering
Candidate No:
Unit 3: Mathematics for Engineering Technicians
Task:
Assignment 4: Sine, Cosine and Tangent ratio tables FACT
SHEET
Grading Criteria: FACT SHEET
Key Skills:
There are three formulae involved in trigonometry
Using Pythagoras
Sine = opposite/hypotenuse
Cosine = adjacent/hypotenuse
Pythagoras’ Theorem using sine, cosine and tangent ratios
Tangent = opposite/adjacent
These can easily be remembered using SOH CAH TOA
Using sine, cosine and tangent tables, calculate the following:
1.
3.
20cm
650
a
2.
15mm
a
Name:
Jo Richardson Community School
BTEC First Diploma in Engineering
Candidate No:
Unit 3: Mathematics for Engineering Technicians
Assignment 4: Solutions to right angle triangle problems
Task: 4b
Grading Criteria: P6
Key Skills:
T
There are three formulae involved in trigonometry
Using Pythagoras
Sine = opposite/hypotenuse
Cosine = adjacent/hypotenuse
Pythagoras’ Theorem using sine, cosine and tangent ratios
Tangent = opposite/adjacent
These can easily be remembered using SOH CAH TOA
Using sine, cosine and tangent tables, calculate the following:
Using the Tangent Ratio Table
1.
3.
650
20cm
a
Using the Cosine Ratio Table
Known – adjacent and hypotenuse values
Cos (angle)
Cos 65
a
a
a
= adjacent / hypotenuse
= a / 20
= cos 65 x 20
= 0.4226 x 20
= 8.45cm
Known – adjacent and opposite values
Tan (angle)
Tan 28
a
a
a
= opposite / adjacent
= a / 15
= tan 28 x 15
= 0.5317 x 15
= 7.98mm
Using the Sine Ratio Table
2.
Known – opposite and hypotenuse values
15mm
Sin (angle)
Sin 25
Sin25 x a
a
a
a
a
Name:
Jo Richardson Community School
BTEC First Diploma in Engineering
= opposite / hypotenuse
= 15 / a
= 15
= 15 / sin25
= 15 / 0.4226
= 35.49m
Candidate No:
Unit 3: Mathematics for Engineering Technicians
Assignment 4: Solutions to right angle triangle problems
Task: 4b
Grading Criteria: P6
Key Skills:
T
Using trigonometry to solve complex shapes
Calculate the length of VA
Name:
Jo Richardson Community School
BTEC First Diploma in Engineering
Candidate No:
Unit 3: Mathematics for Engineering Technicians
Assignment 4: Using trigonometry to solve complex shapes
Task: 4c
Grading Criteria: M4
Key Skills:
Using trigonometry to solve complex shapes
Calculate the length of VA
Name:
Jo Richardson Community School
BTEC First Diploma in Engineering
Candidate No:
Unit 3: Mathematics for Engineering Technicians
Assignment 4: Using trigonometry to solve complex shapes
Task: 4c
Grading Criteria: M4
Key Skills:
T