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Foundations and Pre-Calculus Math 10
Name:___________________________
Chapter 2: Trigonometry
Assignment Checklist
Block:___________________________
Each assignment must have:
-
Title – section, page number and questions
Questions written down
Work shown
Answers marked
Corrections done
A mark out of 5
Assignments
Section
Questions
2.1 The Tangent Ratio
Pg 75-77 # 3, 4, 8 – 14, 17 – 21
2.2 Using the Tangent
Ratio to Calculate
Lengths
Pg 82-83 # 3 – 5 (a & c), 6 – 14, 15
2.3 Measuring an
Inaccessible Height
Project
2.4 The Sine and Cosine
Ratios
Pg 95-96 # 4 – 10, 12 – 15
2.5 Using the Sine and
Cosine Ratios to
Calculate Lengths
Page 101-102 # 3 – 14
2.6 Applying the
Trigonometric Ratios
Page 111 # 3 – 14
2.7 Solving Problems
Involving More than
One Right Triangle
Pg 118-121 #3 – 9, 14
Date Assigned
Total
Please have assignments in this order stapled together with this page on top.
Due: _____________________
Mark
Ch 2 Glossary
Acute angle
Adjacent
Angle of depression
Angle of elevation/inclination
Complementary angles
Cosine
Hypotenuse
Inverse
Obtuse angle
Opposite
Pythagorean Theorem
Ratio
Right Angle
Right Triangle
Sine
Supplementary angles
Tangent
Trigonometric Ratios
Naming the Sides of a Right Triangle
TOOLKIT: 2.1 The Tangent Ratio
SUMMARY:
Recall the three trig ratios: Sin, Cos, Tan
SOH CAH TOA
Make sure that your calculator is set to degrees
If <A is an acute angle in a right triangle, then
tan A =
opposite
adjacent
hyp
opp
A
adj
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑠𝑖𝑑𝑒 𝑙𝑒𝑛𝑔𝑡ℎ
Tangent Ratio: 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒 𝑙𝑒𝑛𝑔𝑡ℎ
To find an angle using the tangent ratio, you must first know the ratio of the opposite and adjacent side (express
this as a decimal).
Use the 𝑇𝑎𝑛−1 or Inverse Tan button on your scientific calculator – make sure you are in degrees!!!
Questions/Main Ideas:
Ex 1: In the right triangle,
calculate the following:
C
11cm
B
18cm
A
A) tan A and < A
B) tan C and < C
Notes:
Ex 2: Ex. Find the angle
A) tan A = 0.4
B) tan A = 4/5
C) tan A = 0.9528
Ex 3:
Ex 4: A support cable is
anchored to the ground 5m
from the base of a telephone
pole. The cable is 19m long. It
is attached at the top of the
pole. What angle, to the
nearest degree, does the cable
make with the ground?
Assignment
Pearson: Page 75 # 3 & 4, 8 – 14, 17 – 21
TOOLKIT: 2.5
2.2 Sine
2.4
Tangent
The
Sine
and to
Cosine
and
Calculate
Cosine
to Calculate
Ratios
Sides Sides
SUMMARY:
SUMMARY:
SUMMARY:
RecallCAH
SOH
the Tangent
TOA Ratio from yesterday.
x
hyp
opposite
opp
opp
tan
0.5x
hyp
Sin AA= 
adjacent
hyp
opp
A
Sin A = 0.5
A
adj
adj
x missing side
Coscan
A also
 use the tangent ratio tohyp
We
find
hyp
lengths
A
adj
0.7x
Direct Measurement: Use a measuring
instrument (protractor, measuring tape etc…) to determine a specific
Cos A = 0.7
value
(angles
or
side
lengths)
**Remember to use shift key for angles**
**Remember that you are not using the shift key to find side lengths**
Indirect Measurement: use mathematical reasoning and logic to determine specific values (angles or side
Questions/Main
Ideas:
Notes:
lengths)
Questions/Main Ideas:
Notes:
Ex.
Ex
1:
1:In
Calculate
triangle the
GHJ,
following:
identify
Questions/Main
Ideas:
the Sin
A)
following:
43
B) Cos 43
Ex
1:
theG;
ratio
a) Sin
G,
Cos
∠Glength of
Ex.
2:Find
Calculate
the
PQ
to J,
theCos
nearest
b) Sin
J; ∠Jtenth of a
A)
cm:tan 16
B) tanP 42
C)Htan 25
J
Ex
2: Find the
length of XY to
10.4m
15cm
the nearest tenth
of a cm.
17cm
Y
67° R
Q
5cm
X
70° a radar station, the
G From
Ex 3:
Z
angle
of elevation of an
Ex 2: An observer
is sitting
on.
approaching
airplane
is 32.5
aThe
dock
watching
a
float
plane
horizontal distance
in
Harbour.
At a
between
plane
and the
ExVancouver
3: In the
Right
triangle
PQR,
certain
time,
the
plane
is
300m
radar
station
is
35.6
km.
<R=90, <Q = 25, and PRHow
=
above
theplane
waterfrom
and
430m
far
the
the radar
7cm.is Determine
the length
of
from
the
observer.
What
is
the
station
to
the
nearest
tenth
of a
QR to the nearest millimeter.
angle of elevation of the plane
kilometer?
measure from the observer, to
the nearest degree?
Notes:
Ex 4: A forest technician is
collecting data about the
heights of trees. She paces a
distance of 15m from the base
of the tree and uses a
clonometer to measure the
angle of elevation to the top of
the tree. The angle is 25. The
technician’s eye is about 1.5m
above the ground. Assume that
the ground is level. How tall is
the tree?
Ex 5: At a horizontal distance
of 200m from the base of an
observation tower, the angle
between the ground and that
line of sight to the top of the
tower is 8°. How high is the
tower to the nearest tenth of a
metre. Sketch a diagram to
help you solve the problem.
Assignment
Pearson: Page 82 # 3 – 5 (a & c), 6 – 14, 15
TOOLKIT:
TOOLKIT: 2.7
2.6 Solving
ApplyingProblems
Trig Ratios
Involving More
than One Right Triangle
SUMMARY:
Continue
Use
your trig
using
tools
yourtotrig
solve
tools:
right triangles: Sin, Cos,
Tan , Pythagoras and other properties of triangles
Sin, Cos, Tan, Pythagoras etc…
Remember, draw a model/picture to help you
visualize
Draw
diagrams
the problem.
where necessary
When we are told to “solve” a right triangle, we are
being asked to find all unknown measures in that
triangle.
Questions/Main Ideas:
Ex. 1: Two office towers are
Questions/Main
50m
apart. From theIdeas:
14th floor
of
tower, the
Ex.the
1: shorter
Solve triangle
ABCangle
of
elevation
to=the
top BC
of the
given
that AC
5cm,
=
taller
tower
is
33
degrees.
The
2cm and <B = 90°
angle of depression to the base
of the taller tower is 39
degrees. Determine the height
of the taller tower.
Ex. 2: Solve triangle XYZ given
XY = 9m, <Y = 90 and <Z =
36
Ex. 2: As part of a weekend
expedition, an Adventurer’s
Club proposes to climb a cliff
overlooking a river. To plan
for the climb, a surveyor took
Ex
3: measurements
Lighthouse park
some
to is 7km
due north the
of Tower
in
calculate
height Beach
of the cliff.
Vancouver.
A
sailboat
leaves
From a point R on the shore
Lighthouse
Parktheonriver,
a bearing
directly
across
the
of
211
degrees.
When
the
angle of elevation to the top of
sailboat
due west
of Tower
the
cliff isis <TRB
= 43°.
From
straight
aBeach,
point itS,turns
30m down
river,
towards
Howthe
far
<BSR = the
69°.beach.
Calculate
does the
travel?
height
ofboat
the cliff.
Notes:
Notes: