Unit 5: Trigonometry
Day 3: Solving Oblique Triangles with Sine and Cosine Laws
Time Bar:
Minds On: 10
Math Learning Goals: Students will;
40 

Consolidate:
20

Action:
Minds On…
15 minutes
identify and label sides and angles of oblique triangles.
solve 2D problems involving oblique triangles using the Sine Law and
the Cosine Law
know when to use either the Sine Law or the Cosine Law to solve such problems
MCR3U1
Gr. 11 University
Materials
 Lesson 5-4 handout
 Chart paper,
markers , tape
 Concept map labels
 Exit ticket
 SRS units
 Lesson files
 SMARTBoardTM
Whole Class  Engage/ Reason to Learn
Engage multiple
intelligences of
visual, linguistic,
and kinaesthetic
learners with the
use of cards to
review relevant
terminology.
Motivate Student Interest: Discuss the need to use trigonometry in sports and
in a career which relies on knowledge of trigonometry. (hockey, city planning)
Placemat: Developing Learning Goals
Pose a question -Within what angle must the hockey player shoot the puck to
score? What do you need to solve the problem?
Think/Pair/Share:
Action!
40 minutes
Collaborative Problem-Based Inquiry

Present the problem to solve without giving all required information.
Students discuss what they would need to know to answer the question.
Solution to be completed as an exit ticket at the end of the lesson.

Students recall Sine and Cosine Laws from Gr. 10 Academic Math Course
Build interpersonal
intelligence during
group activity.
Small Groups  Collaborative Problem Solving

Students investigate the options provided to determine when to use each
of the sine and cosine law in preparation for 2D trig problem solving.

Teacher poses questions to expose thinking, listens, observes, offers
prompts when necessary as students complete investigation.
Whole Class  Sharing and Summarizing Key Concepts

Concept map constructed and presented by students and kept as a visual
summary of investigation for student reference on word wall.

Process:
Mathematical
Process: Reflecting
, Representing
Students complete practice examples with teacher direction
and selected students share results on whiteboard with classmates.
Consolidate
Debrief
Individual  Consolidate

Exit Ticket and/or SRS units used to assess understanding and skill
development
20 minutes
Practice
Skill Drill
Home Activity

Students practice concepts presented using handout assignment.
Handout: “Practice” #2ace, 3ace, 4ac, 10, 11, 17

Assessment for
learning
(inform future
instruction)
Lesson 5-4:
Solving Oblique (Non-Right) Triangles with
The Sine and Cosine Laws
(attanasiomath.wikispaces.com)
Investigate The Sine and Cosine Law
Recall: The Sine and Cosine Laws are used when solving non-right triangles, also called OBLIQUE
triangles. For right triangles we use the Pythagorean Theorem or the Trig Ratios (SOH CAH TOA).
1.
Label the sides of the triangle and complete the Sine and Cosine Laws below:
Sine Law
𝑎
sin 𝐴
=
Cosine Law
=
a2 = b2 + c2 – 2bc cos
or
OR
b2 = a 2 + c 2 –
or
sin 𝐴
𝑎
2.
=
=
c2 =
Complete the table below to determine when to use each law.
Diagram
Information Given
(S = side, A = angle)
Law Used
(Sine or Cosine)
Ex. 1: The Leaning Tower of Pisa is 56m tall and 4° from the vertical. If a support beam must
be placed 30m from the center of the Tower for safety reasons, what is the length of the
beam needed to support the Tower during repairs?
Ex. 2: A triangular plot of land is situated between three roads. What angle will be made between
the two roads at A?
B
4.2km
4.7km
C
A
6.9km
Ex. 3: Phineas and Ferb were measuring the height of a cloud directly above them. The results
from the clinometer are given below. How high is the cloud above them?
C
20o
50o
A
Homefun: Handout “Practice” #2ace, 3ace, 4ac, 10, 11, 17
350m
m
B
Exit Ticket: What did you learn?
Name:
Dion Phaneuf is attempting to score by shooting the puck along the ice from a point some
distance in front of the net. Within what angle must he shoot the puck?
1. What information do you need?
A
2. Solve the problem.
Extra Practice:
Triangle
What to Use?
Pythagorean Theorem | SOH CAH TOA |
Sine Law | Cosine Law
B
If I was finding the length of side a, I would use
25 cm
________________________________
a
20°
A
40 cm
C
P
If I was finding the length of side p, I would use
________________________________
124
74
Q
R
p
If I was finding the length of side x, I would use
________________________________
M
83
L
If I was finding the value of angle K, I would use
________________________________
74
110

K