Download Chapter 14 Work program

1
WORK PROGRAM  MQ 9 NSW 5.2 Pathway
Chapter 14 Right-angled trigonometry
Strand: 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
Trigonometry
MS5.2.3 Applies trigonometry to solve problems including those involving bearings
Two-dimensional space
SGS3.2b Measures, constructs and classifies angles
Position
SGS3.3 Uses a variety of mapping skills
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 484)
GC tips, Investigations,
History of mathematics,
Maths Quest challenge,
10 Quick Questions,
Code puzzles
SkillSHEETS,
WorkSHEETS,
Interactive games,
Test yourself, Topic tests
(CD–ROM)
SkillSHEETS (page 484)
14.1: Measuring angle
with a protractor
14.3: Rounding to a given
number of decimal
places
14.4: Solving equations of
x
the type a =
to find x
b
14.5: Solving equations of
b
the type a =
to find x
x
Technology applications
(CD–ROM)
Learning outcomes
SGS3.2b
 using a protractor to
measure angles
SGS 3.3
 locating a place on a
map which is a given
direction from a
landmark
SGS4.3
 recognising and
classifying types of
triangles on the basis
2
14.10: Using Pythagoras’
theorem
14.11 Identifying and
using properties of a
triangle
14.12: Understanding
direction
What is trigonometry?
(page 485)
Naming the sides of a
right-angled triangle
(page 485)
WE 1, 2, 3a-c
Ex 14A Naming the sides
of a right-angled triangle
(page 490)
Investigation: The cosine
and tangent ratios
(page 488)
Maths Quest challenge:
Q1 (page 493)
SkillSHEET 14.1:
Measuring angles with
a protractor (page 491)
Game time 001 (page 493)
Cabri geometry:
Investigating the sine
ratio (page 486)
Cabri geometry:
Investigating the cosine
ratio (page 489)
Cabri geometry:
Investigating the tangent
ratio (page 489)
of their properties
(acute-angled, rightangled, obtuse-angled,
scalene, isosceles and
equilateral triangles)
MS4.1
 using Pythagoras’
theorem to find the
length of sides in rightangled triangles
NS4.3
 rounding decimals to a
given number of places
PAS4.4
 solving equations
using algebraic
methods that involve
up to and including
three steps in the
solution process and
have solutions that are
not necessarily whole
numbers
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
3
Cabri geometry: Sine,
cosine, tangent
(page 491)
Trigonometric ratios
(page 494)
WE 4, 5a-b
Ex 14B Trigonometric
ratios (page 496)
Maths Quest challenge:
Q1 (page 498)
SkillSHEET 14.2:
Labelling sides of a
triangle (page 496)
SkillSHEET 14.3:
Rounding to a given
number of decimal
places (page 497)
WorkSHEET 14.1
(page 498)
Mathcad: Trigonometric
ratios (page 496)
Excel: Introducing the trig
ratios (page 497)
ratio of matching sides
in similar right-angled
triangles is constant for
equal angles
 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)
 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
4
Finding trigonometric
ratios using a calculator
(page 499)
WE 6a-c
Ex 14C Finding
trigonometric ratios
using a calculator
(page 500)
Finding side lengths
(page 500)
WE 7, 8
Ex 14D Finding side
lengths (page 502)
GC tip – Casio: Finding
sin, cos or tan of an
angle (page 499)
Angles and the calculator
(page 505)
WE 9a-b, 10, 11a-b
Ex 14E Angles and the
GC tip – Casio: Finding
DMS or  ‘ “ on a
graphics calculator
Maths Quest challenge:
Q1 (page 504)
SkillSHEET 14.4: Solving
equations of the type
x
a = to find x
b
(page 502)
SkillSHEET 14.5: Solving
equations of the type
b
a = to find x
x
(page 503)
SkillSHEET 14.6:
Rearranging formulas
(page 503)
Game time 002 (page 504)
WorkSHEET 14.2
(page 504)
SkillSHEET 14.7:
Rounding angles to the
nearest degree
(page 508)
GC tip – TI: Finding sin,
cos or tan of an angle
(page 499)
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
Excel: Using sine
(page 502)
Excel: Using cosine
(page 502)
Excel: Using cosine (DIY)
(page 503)
Excel: Using tangent
(page 503)
Excel: Using tangent
(DIY) (page 503)
Excel: Universal
trigonometric calculator
(page 503)
Mathcad: Finding side
lengths (page 503)
MS5.1.2
 using trigonometric
notation e.g. sin A
 selecting and using
appropriate
trigonometric ratios in
right-angled triangles
to find unknown sides,
including the
hypotenuse
 solving problems in
practical situations
involving right-angled
triangles (Applying
strategies)
GC program – TI:
Entering angles
expressed in degrees,
minutes and seconds
MS5.1.2
 using a calculator to
find approximations of
5
calculator (page 508)
Finding the size of an
angle (page 509)
WE 12a-b, 13a-b
Ex 14F Finding the size of
an angle (page 513)
(page 505)
GC tip – Casio:
Converting degrees in
decimal form to
degrees, minutes and
seconds (page 507)
Maths Quest challenge:
Q1-2 (page 508)
10 Quick Questions 1
(page 509)
10 Quick Questions 2
(page 514)
Code puzzle (page 515)
SkillSHEET 14.8:
Rounding angles to the
nearest minute
(page 508)
SkillSHEET 14.9:
Rounding angles to the
nearest second
(page 508)
(page 505)
GC program – TI:
Converting degrees in
decimal form to degrees,
minutes and seconds
(page 507)
Excel: Converting angles
(page 508)
Mathcad: Finding angles
(page 513)
Excel: Finding angles
(page 513)
the trigonometric ratios
of a given angle
measured in degrees
 using a calculator to
find an angle correct to
the nearest degree,
given one of the
trigonometric ratios of
the angle
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
MS5.1.2
 selecting and using
appropriate
trigonometric ratios in
right-angled triangles
to find unknown
angles correct to the
nearest degree
MS5.2.3
 using trigonometric
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Applications (page 516)
WE 14a-c, 15
Ex 14G Applications
(page 518)
Investigation: Using an
SkillSHEET 14.10: Using
inclinometer to measure
Pythagoras’ theorem
inaccessible heights
(page 518)
(page 520)
SkillSHEET 14.11:
Identifying and using
properties of a triangle
(page 518)
WorkSHEET 14.3
(page 519)
Excel: Universal
trigonometric calculator
(page 519)
ratios to find unknown
angles in degrees and
minutes in right-angled
triangles
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
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
 solving problems in
practical situations
involving right-angled
triangles (Applying
strategies)
7

interpreting diagrams
in questions involving
angles of elevation and
depression
(Communicating)
MS5.2.3
 finding unknown sides
in right-angled
triangles where the
given angle is
measured in degrees
and minutes
 using trigonometric
ratios to find unknown
angles in degrees and
minutes in right-angled
triangles
 drawing diagrams and
using them to solve
word problems which
involve angles of
elevation and
depression
 solving practical
problems involving
angles of elevation and
depression (Applying
strategies)
 checking the
reasonableness of
answers to
trigonometry problems
8
Bearings (page 521)
WE 16a-b, 17a-b, 18a-c
Ex 14H Bearings
(page 524)
History of mathematics:
George Everest
(page 526)
SkillSHEET 14.12:
Mathcad: Converting to
Understanding direction
true bearings (page 524)
(page 524)
SkillSHEET 14.13:
Drawing a diagram
from given directions
(page 525)
(Reasoning)
MS5.2.3
 finding unknown sides
in right-angled
triangles where the
given angle is
measured in degrees
and minutes
 using trigonometric
ratios to find unknown
angles in degrees and
minutes in right-angled
triangles
 using three-figure
bearings (e.g. 035,
225) and compass
bearings e.g. SSW
 drawing diagrams and
using them to solve
word problems which
involve bearings
 solving simple
problems involving
three-figure bearings
(Applying strategies,
Communicating)
 recognising directions
given as SSW, NE etc.
(Communicating)
 interpreting directions
given as bearings
(Communicating)
9
Summary (page 527)
Chapter review (page 528)
‘Test yourself’ multiple
choice questions
(page 530)
Topic tests (2)