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WORK PROGRAM
Chapter 10 Right-angled trigonometry
Strands: Measurement, Space and geometry, Number, Patterns and algebra
Substrands and outcomes:
Perimeter and area
MS4.1 Uses formulae and Pythagoras’ theorem in calculating perimeter and area of circles and
figures composed of rectangles and triangles
Trigonometry
MS5.1.2 Applies trigonometry to solve problems (diagram given) including those involving angles
of elevation and depression
Two-dimensional space
SGS3.2b Measures, constructs and classifies angles
Properties of geometrical figures
SGS4.3 Classifies, constructs, and determines the properties of triangles and quadrilaterals
Fractions, decimals and percentages
NS4.3 Operates with fractions, decimals, percentages, ratios and rates
Algebraic techniques
PAS4.4 Uses algebraic techniques to solve linear equations and simple inequalities
Section
Are you ready? (page 296)
GC tips, Investigations,
History of mathematics,
Maths Quest challenge,
10 Quick Questions,
Code puzzles,
Career profiles
SkillSHEETs,
WorkSHEETs,
Interactive games,
Test yourself, Topic tests
(CD-ROM)
SkillSHEETs (page 296)
10.1: Measuring angles
with a protractor
10.3: Rounding to a given
number of decimal
places
10.4: Solving equations of
x
the type a = to find x
b
10.5: Solving equations of
b
the type a = to find x
x
10.8: Using Pythagoras’
theorem
10.9: Identifying and using
Technology applications
(CD-ROM)
Learning outcomes
SGS3.2b
 using a protractor to
measure angles
NS4.3
 rounding decimals to a
given number of
decimal places
PAS4.4
 solving equations
using algebraic
methods
MS4.1
 using Pythagoras’
theorem to find the
length of sides in rightangled triangles
1
properties of a triangle
What is trigonometry?
(page 297)
Naming the sides of a
right-angled triangle
(page 297)
WE 1, 2, 3a-c
Ex 10A Naming the sides
of a right-angled triangle
(page 302)
Investigation: The cosine
and tangent ratios
(page 300)
SkillSHEET 10.1:
Measuring angles with a
protractor (page 303)
Game time 001 (page 305)
Cabri geometry:
Investigating the sine
ratio (page 298)
Cabri geometry:
Investigating the cosine
ratio (page 301)
Cabri geometry:
Investigating the tangent
ratio (page 301)
Cabri geometry: Sine,
cosine, tangent
(page 303)
SGS4.3
 recognising and
classifying types of
triangles on the basis
of their properties
MS5.1.2
 identifying the
hypotenuse, adjacent
and opposite sides with
respect to a given
angle in a right-angled
triangle in any
orientation
 recognising that the
ratio of matching sides
in similar right-angled
triangles is constant for
equal angles
 labelling the side
lengths of a rightangled triangle in
relation to a given
angle e.g. the side c is
opposite angle C
 defining the sine,
cosine and tangent
ratios for angles in
right-angled triangles
 labelling sides of rightangled triangles in
different orientations
in relation to a given
angle (Applying
strategies,
Communicating)
2

Trigonometric ratios
(page 306)
WE 4, 5a-b
Ex 10B Trigonometric
ratios (page 308)
Maths Quest challenge
(page 305)
Finding trigonometric
ratios using a calculator
(page 311)
WE 6a-c
Ex 10C Finding
trigonometric ratios
using a calculator
(page 312)
Finding side lengths
(page 312)
WE 7, 8
Ex 10D Finding side
lengths (page 314)
GC tip  Casio: Finding
sin, cos or tan of an angle
(page 311)
Maths Quest challenge
Q1 (page 316)
10 Quick Questions 1
(page 317)
SkillSHEET 10.2:
Mathcad: Trigonometric
Labelling sides of a
ratios (page 308)
triangle (page 308)
Excel: Introducing the trig
SkillSHEET 10.3:
ratios (page 309)
Rounding to a given
number of decimal places
(page 309)
WorkSHEET 10.1
(page 310)
GC tip  TI: Finding sin,
cos or tan of an angle
(page 311)
SkillSHEET 10.4: Solving
equations of the type
x
a = to find x (page 314)
b
SkillSHEET 10.5: Solving
equations of the type
Excel: Using sine
(page 314)
Excel: Using cosine
(page 314)
Excel: Using cosine (DIY)
(page 315)
explaining why the
ratio of matching sides
in similar right-angled
triangles is constant for
equal angles
(Communicating,
Reasoning)
MS5.1.2
 defining the sine,
cosine and tangent
ratios for angles in
right-angled triangles
 using trigonometric
notation e.g. sin A
 labelling sides of rightangled triangles in
different orientations
in relation to a given
angle (Applying
strategies,
Communicating)
MS5.1.2
 using a calculator to
find approximations
of the trigonometric
ratios of a given angle
measured in degrees
MS5.1.2
 selecting and using
appropriate
trigonometric ratios in
right-angled triangles
to find unknown sides,
3
Excel: Using tangent
(page 315)
Excel: Using tangent
(DIY) (page 315)
Excel: Universal
trigonometric calculator
(page 315)
Mathcad: Finding side
lengths (page 315)
SkillSHEET 10.7:
Mathcad: Finding angles
Rounding angles to the
(page 320)
nearest degree (page 320) Excel: Finding angles
(page 320)
b
to find x (page 315)
x
SkillSHEET 10.6:
Rearranging formulas
(page 315)
Game time 002 (page 316)
WorkSHEET 10.2
(page 316)
a=
Finding the size of an
angle (page 317)
WE 9a-c
Ex 10E Finding the size of
an angle (page 320)
10 Quick Questions 2
(page 321)
Code puzzle (page 322)
Applications (page 323)
WE 10a-c, 11
Ex 10F Applications
(page 326)
Investigation: Using an
inclinometer to measure
inaccessible heights
(page 328)
History of mathematics:
George Everest
(page 329)
SkillSHEET 10.8: Using
Pythagoras’ theorem
(page 326)
SkillSHEET 10.9:
Identifying and using
properties of a triangle
(page 326)
WorkSHEET 10.3
(page 327)
Excel: Universal
trigonometric calculator
(page 326)

including the
hypotenuse
solving problems in
practical situations
involving right-angled
triangles (Applying
strategies)
MS5.1.2
 using a calculator to
find an angle correct
to the nearest degree,
given one of the
trigonometric ratios of
the angle
 selecting and using
appropriate
trigonometric ratios in
right-angled triangles
to find unknown
angles correct to the
nearest degree
MS5.1.2
 selecting and using
appropriate
trigonometric ratios in
right-angled triangles
to find unknown sides,
including the
hypotenuse
 selecting and using
appropriate
trigonometric ratios in
right-angled triangles
4




Summary (page 330)
Chapter review (page 331)
to find unknown
angles correct to the
nearest degree
identifying angles of
elevation and
depression
solving problems
involving angles of
elevation and
depression when
given a diagram
interpreting diagrams
in questions involving
angles of elevation
and depression
(Communicating)
solving problems in
practical situations
involving right-angled
triangles (Applying
strategies)
‘Test yourself’ multiple
choice questions
Topic tests (2)
5