Unit 5: TrigonometryDay 3: Solving Oblique Triangles with Sine and Cosine Laws

MCR3U1Gr. 11 University

Time Bar:Minds On: 10Action: 40Consolidate: 20

Math Learning Goals: Students will;

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

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

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: 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

Engage multiple intelligences of visual, linguistic, and kinaesthetic learners with the use of cards to review relevant terminology.

Build interpersonal intelligence during group activity.

Minds On…

15 minutes

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.

Students complete practice examples with teacher direction and selected students share results on whiteboard with classmates.

Process: Mathematical Process: Reflecting , Representing

Action!

40 minutes

Individual Consolidate Exit Ticket and/or SRS units used to assess understanding and skill

development

Assessment for learning (inform future instruction)

Consolidate Debrief

20 minutes

PracticeSkill Drill

Home Activity Students practice concepts presented using handout assignment.

Handout: “Practice” #2ace, 3ace, 4ac, 10, 11, 17

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 Cosine Law

asin A

=❑=❑ a2 = b2 + c2 – 2bc cos

orOR b2 = a2 + c2 –

orsin Aa

=❑=❑ c2 =

2. Complete the table below to determine when to use each law.

Diagram Information Given(S = side, A = angle)

Law Used(Sine or Cosine)

C

4.7km4.2km

6.9km

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?

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?

B

A

A

C

B350m m

50o 20o

Homefun: Handout “Practice” #2ace, 3ace, 4ac, 10, 11, 17

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?

2. Solve the problem.

A

a

20°

CA

B

40 cm

25 cm

Extra Practice:

Triangle What to Use?Pythagorean Theorem | SOH CAH TOA |

Sine Law | Cosine Law

If I was finding the length of side a, I would use

________________________________

74

p

124

RQ

PIf I was finding the length of side p, I would use

________________________________

If I was finding the length of side x, I would use

________________________________

110

83

74

M

L

K

If I was finding the value of angle K, I would use

________________________________