WORK PROGRAM
Chapter 14 Trigonometry
Strand: Measurement
Substrands and outcomes:
Trigonometry
MS5.1.2 Applies trigonometry to solve problems (diagrams given) including those involving angles of elevation
and depression
Trigonometry
MS5.2.3 Applies trigonometry to solve problems including those involving bearings
Trigonometry
MS5.3.2 Applies trigonometric relationships, sine rule, cosine rule and area rule in problem solving
Section
Are you ready? (page 530)
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 530)
14.1: Labelling rightangled triangles
14.2: Calculating sin, cos
or tan of an angle
14.4: Finding side lengths
in right-angled triangles
14.5: Calculating the angle
from a sin, cos or tan
ratio
14.6: Finding angles in
right-angled triangles
Technology applications
(CD-ROM)
Learning outcomes
MS5.1.2
 identifying the
hypotenuse, adjacent
and opposite sides with
respect to a given
angle, in a right-angled
triangle in any
orientation
 selecting and using
appropriate
trigonometric ratios in
right-angled triangles
to find unknown sides
 using a calculator to
find an angle correct to
the nearest degree,
given one of the
trigonometric ratios of
the angle
MS5.2.3
1

Trigonometry of rightangled triangles
(page 531)
WE 1, 2, 3, 4
Ex 14A Trigonometry of
right-angled triangles
(page 535)
Investigation:
Trigonometric identities
(page 537)
SkillSHEET 14.1: Labeling Mathcad: Triangle
right-angled triangles
(page 535)
(page 535)
Cabri geometry: SOH
SkillSHEET 14.2:
CAH TOA (page 535)
Calculating sin, cos or
tan of an angle
(page 535)
SkillSHEET 14.3:
Rearranging
trigonometric equations
(page 535)
SkillSHEET 14.4: Finding
side lengths in rightangled triangles
(page 535)
SkillSHEET 14.5:
Calculating the angle
from a sin, cos or tan
ratio (page 535)
SkillSHEET 14.6: Finding
angles in right-angled
triangles (page 535)
SkillSHEET 14.7:
Composite shapes I
using a calculator to
find trigonometric
ratios of a given
approximation from
angles measured in
degrees and minutes
 using trigonometric
ratios to find unknown
angles in degrees and
minutes in right-angled
triangles
MS5.1.2
 identifying the
hypotenuse, adjacent
and opposite sides with
respect to a given angle,
in a right-angled
triangle in any
orientation
 using trigonometric
notation
 using a calculator to
find approximations of
the trigonometric ratios
of a given angle
measured in degrees
 selecting and using
appropriate
trigonometric ratios in
right-angled triangles to
find unknown sides,
including the
hypotenuse
 selecting and using
appropriate
2
(page 536)
SkillSHEET 14.8:
Composite shapes II
(page 536)
Game time 001 (page 537)
trigonometric ratios in
right-angled triangles to
find unknown angles
correct to the nearest
degree
 labeling sides of rightangled triangles in
different orientations in
relation to a given angle
(Applying strategies,
Communicating)
 solving problems in
practical situations
involving right-angled
triangles e.g. finding
the pitch of a roof
(Applying strategies)
MS5.2.3
 using a calculator to
find trigonometric
ratios of a given
approximation for
angles measured in
degrees and minutes
 using a calculator to
find an approximation
for an angle in degrees
and minutes, given the
trigonometric ratio of
the angle
 finding unknown sides
in right-angled triangles
where the given angle
is measured in degrees
and minutes
3
Applications of rightangled triangles
(page 537)
WE 5, 6a-b, 7, 8
Ex 14B Applications of
right-angled triangles
(page 541)
Investigation: Fly like a
bird (page 543)
Code puzzle (page 544)
Game time 002 (page 543)
WorkSHEET 14.1
(page 543)
Mathcad: SOH CAH TOA
(page 541)
Cabri geometry: Triangle
(page 541)
 using trigonometric
ratios to find unknown
angles in degrees and
minutes in right-angled
triangles
 checking the
reasonableness of
answers to
trigonometry problems
(Reasoning)
MS5.2.3
 using three-figure
bearings and compass
bearings
 drawing diagrams and
using them to solve
word problems which
involve bearings or
angles of elevation and
depression
 solving simple
problems involving
three-figure bearings
(Applying strategies,
Communicating)
 recognising directions
given as SSW, NE etc
(Communicating)
 interpreting directions
given as bearings
(Communicating)
 solving practical
problems involving
angles of elevation and
depression (Applying
4
Problems involving two
right-angled triangles
(page 545)
WE 9
Ex 14C Problems
involving two rightangled triangles
(page 547)
Non-right-angled triangles
– the sine rule (page 548)
WE 10, 11
Ex 14D Non-right-angled
triangles – the sine rule
(page 551)
Non-right-angled triangles
– the cosine rule
10 Quick Questions 1
(page 553)
SkillSHEET 14.9: Using
Pythagoras’ theorem
(page 547)
Excel: Universal
trigonometric calculator
(page 547)
WorkSHEET 14.2
(page 553)
Mathcad: Sine rule
(page 551)
Mathcad: Cosine rule
(page 557)
strategies)
MS5.3.2
 using appropriate
trigonometric ratios
and formulae to solve
two-dimensional
trigonometric
problems that require
the use of more than
one triangle, where the
diagram is provided,
and where a verbal
description is given
(Applying strategies)
MS5.1.2
 labelling the side
lengths of a rightangled triangle in
relation to a given
angle e.g. the side c is
opposite angle C
MS5.3.2
 proving the sine rule
 drawing diagrams and
using them to solve
word problems that
involve non-rightangled triangles
 solving problems,
including practical
problems, involving the
sine rule (Applying
strategies)
MS5.1.2
 labelling the side
5
(page 554)
WE 12, 13, 14
Ex 14E Non-right-angled
triangles – the cosine rule
(page 557)
Area of triangles
(page 558)
WE 15, 16, 17
Ex 14F Area of triangles
(page 561)
10 Quick Questions 2
(page 564)
Investigation: Which way
do I go? (page 565)
Maths Quest challenge:
Q1 (page 565)
WorkSHEET 14.3
(page 563)
Mathcad: Area of a
triangle (page 561)
lengths of a rightangled triangle in
relation to a given angle
e.g. the side c is
opposite angle C
MS5.3.2
 proving the cosine rule
 using the cosine rule to
find unknown sides and
angles of a triangle
 drawing diagrams and
using them to solve
word problems that
involve non-rightangled triangles
 solving problems,
including practical
problems, involving the
sine and cosine rules
(Applying strategies)
MS5.1.2
 labelling the side
lengths of a rightangled triangle in
relation to a given angle
e.g. the side c is
opposite angle C
MS5.3.2
 proving and using the
area rule to find the
area of a triangle
 drawing diagrams and
using them to solve
word problems that
involve non-right6
angled triangles
 solving problems,
including practical
problems, involving the
sine and cosine rules
and the area rule
(Applying strategies)
Summary (page 566)
Chapter review (page 568)
‘Test yourself’ multiple
choice questions
Topic tests (2)
7