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MPM 2D Principals of Mathematics
Grade 10 Academic Mitchell District High School
Unit 1 Trigometry 9 Video Lessons
Allow no more than 15 class days for this unit!
This includes time for review and to write the test. This does NOT include time for days absent, including snow days. You must
make sure you catch up on class days missed.
Lesson # Lesson Title Practice Questions Date Completed
1 Geometric Concepts Page 315 #(1, 2)every other, 3, 4
2 Similar Triangles - Part 1 Similar Triangles - Part 2
Page 322 #1 - 3, 5, 6
3 Similar Triangle Problems - Part 1 Similar Triangle Problems - Part 2
Page 324 #5 - 10, 15
4 Pythagorean Theorm Similarity Proofs
Page 323 #2 (Prove they are
similar), 4, 5
5 Primary Trig Ratios - Part 1 Primary Trig Ratios - Part 2 Primary Trig Ratios - Part 3
Page 348 #1, 2 + handout
6 Applications of Primary Trig Ratios
Page 348 #3-11
7 The Sine Law Page366 #(1-5)a) c) 6, 8, 12
8 The Cosine Law Page 373 #1b), 2b), 3a)c) 4a), 5, 6, 8
9 Solving Problems with Multiple Triangles
Page 355 #1, 5, 8, 12, 13, 15, 16
Test Written on : _______________________________________
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Al Jebra Takes Over Trigonometry The Evil Dr. Al Jebra has been hard at work trying to take all the enjoyment out of the world of mathematics. He has stolen some of the world’s best math jokes and encoded the punch lines using trigonometry. He thinks no one will care enough to wade through all those trig questions to get them back, but your mission is to prove otherwise. Each of the following questions uses sine, cosine or tangent to solve for missing measures of a right triangle. When you have solved for the variable, write its value (rounded to the nearest whole number) in the appropriate box below. Once completed you will have the key to unlocking the math jokes. Give your key to your teacher to check before deciphering the jokes.
Good Luck. The world is counting on you. !
!
A ! B ! C ! D ! E ! F ! G !
H ! I ! J ! K ! L ! M ! N !
O ! P ! Q ! R ! S ! T ! U !
V ! W ! X ! Y ! Z ! ! !
Al#Jebra#Takes#Over#Trigonometry#5#Codes#!Why!was!Mr.!Agar!detained!at!the!airport!on!his!way!to!Iraq?!!18,34!!!43,!22,5!!!!5,!47,!5,!20,!34,!41,!32,!34,!15!!!!!29,!68!!!!!!!18,!22,!30,!58,!8,!63!!!!!43,!34,!22,!20,!29,!8,!5!!!!!29,!68!!!!!54,!22,!32,!18!!!!!!58,!8,!5,!32,!4,!47,!41,!32,!58,!29,!8!_________________________________________________________________________________________!!What!did!one!math!book!say!to!another!math!book?!!
15,!29,!8!’!32!!!!!!!23,!29,!32,!18,!34,!4!!!!!54,!34!!!!!58!!!!!18,!22,!30,!34!!!!!54,!7!!!!!!29,!43,!8!!!!!20,!4,!29,!23,!73,!34,!54,!5.!!!!How!is!2!+!2!=!5!like!an!obtuse!triangle?!!32,!18,!34,!7!!!!!22,!4,!34!!!!!8,!29,!32!!!!!4,!58,!63,!18,!32.!___________________________________________________________________________________________!!Why!did!the!boy!eat!his!math!homework?!!!32,!18,!34!!!!!32,!34,!22,!41,!18,!34,!4!!!!!32,!29,!73,!15!!!!!18,!58,!54!!!!!58,!32!!!!!43,!22,!5!!!!!22!!!!!!20,!58,!34,!41,!34!!!!!29,!68!!!!!41,!22,!12,!34.!___________________________________________________________________________________________!!!!!!!!Dad,!can!you!help!me!find!the!lowest!common!denominator!in!this!problem!please!?!!
15,!29,!8!’!32!!!!!32,!34,!73,!73!!!!!54,!34!!!!!32,!18,!34,!7!!!!!18,!22,!30,!34,!8!!’!32!68,!29,!47,!8,!15!!!!!58,!32!!!!!7,!34,!32!!!!!!!58!!!!!4,!34,!54,!34,!54,!23,!34,!4!!!!73,!29,!29,!12,!58,!8,!63!!!!!68,!29,!4!!!!!58,!32!!!!!43,!18,!34,!8!!!!!58!!!!!43,!22,!5!!!!!22!!!!!23,!29,!7.!__________________________________________________________________________________________!!What!did!zero!say!to!8?!!8,!58,!41,!34!!!!!!23,!34,!73,!32!__________________________________________________________________________________________!!!!!!!!What!happened!when!Mr.!Agar!picked!Opposite!Beach!over!Adjacent!Ski!Slopes!for!his!March!Break!vacation?!!18,!34!!!!!!43,!22,!5!!!!!22!!!!!32,!22,!8!!!!!63,!34,!8,!32!___________________________________________________________________________________________!!!!!!!!!
MPM2D U1L6 Applications of Primary Trig Ratios
Example 1. A helicopter spots a campfire at an angle of depression of 15o. Draw a diagram and mark on the angle of depression.
Today's Topic: Primary Trig Ratios
Today's Goal: to learn terminology related to application question and to be able to effectively use trigonometry to solve problems.
Today's Topic: Primary Trig Ratios
Today's Goal: to learn terminology related to application question and to be able to effectively use trigonometry to solve problems.
Applications Using TrigonometryAngle of Depression: an angle measured down from a horizontal line to
the line of sight between objects.Angle of Elevation: an angle measured up from a horizontal line to the
line of sight between objects.
MPM2D U1L6 Applications of Primary Trig Ratios
Example 2. Kaitlin looks up at an angle of elevation of 75o to see the top of the CN Tower. Draw a diagram and mark on the angle of elevation.
Example 3. A surveyor measures the angle of elevation from his eye to the top of a tree to be 73o. He knows that his eye is 162cm above ground level and he is standing 7 m from the tree when he takes his measurement. How tall is the tree?
MPM2D U1L6 Applications of Primary Trig Ratios
2D Homework
Page 332 #10, 12, 14 Page 339 #10, 11, 13 Page 345 #9, 10, 13
Example 4. A guy wire holds a hydro pole into an upright position. It is attached to the pole at a location 0.5 m from the top, and makes a 63o angle of elevation with the ground. If the guide wire is 6 m long, how tall is the pole?
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MPM 2D Trigonometry Review
Similar Triangles
Two triangles are considered _______________ if all angles are equal.
To show that triangles are similar we need to _______________ the equal
_______________.
If triangles are similar, the ratios of the _______________ sides are _______________.
The ratios of the areas of similar triangles are equal to the ratios of the _______________ of
corresponding sides.
Example 1. a) Find the missing sides b) If the area of ΔABC is 18 cm2 find the area of ΔDEF.
Example 2. Show the following triangles are similar if ABDE
The Primary Trigonometry Ratios
Sine equals _______________ over _______________.
Cosine equals _______________ over _______________.
Tangent equals _______________ over _______________.
To find an angle with our calculator we need to use the _______________ trig functions.
If you don’t need or have the _______________ in a triangle the ratio you use is the tangent.
Example 4. Find x
A
B
C
D
E
F
5 7 26
60
β
β
α θ
α
θ
A
B
C
D
E
Example 5. On the roof of the school if you look up 15° you will
see the top of the flagpole. Look down 55° and you
will see the bottom of the flagpole. If the school is 6.7m from the flagpole…
a) how high is the school? b) how tall is the pole? {Disregard your height as you stand on the roof}
A
D C B 10.5 cm
x
9°
33°
Example 3. a) Find sin R, cos R, and tan R. b) Evaluate angle R.
R
S T
12 c
m
16 cm
Sine Law and Cosine Law
Sine Law is used for _______________ triangles
Cosine Law can be used for either _______________ or _______________ triangles.
Use _______________ Law for a triangle when you know a value for an angle and its
opposite side.
Use _______________ Law if you know an angle and both sides adjacent to it.
The _______________ Law says that for any acute triangle, all the ratios of the sine of an
angle to the side opposite are equal.
For ΔABC Sine Law states:
Where capital letters stand for __________ and lower case letters stand for ______
___________.
For ΔABC the form of Cosine Law that involves ∠A states:
Where b, and c are the sides _______________ to ∠A.
Example. 6 Solve the following triangles.
Example 7. A plane leaves the airport travelling 365 km/h N65°W. Another leaves at the same time
travelling 285 km/h S15°E. After they have been in the air for 2 hours, how far apart are the planes
to the nearest km?
35° 73°
9 m L
M
N
a) b)
14 cm
8 cm 9 cm
Q
R
S
Answers: 1. a) 18.6, 16.2 b) 248.3 cm2 3. a)
b) R=53°
4. 14.9cm 5. a) 9.6 m b) 11.4 m 6. a) 72°, 9.0 m, 5.4 m
b) 111°, 32°, 37°
7. 1180 km