Unlocking Triangles: Mastering the Sine Rule in Algebra 2

Algebra 2 Grades High School 13:06 Video
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Lesson Description

Learn how to solve non-right triangles using the Sine Rule. This lesson covers the formula, application, and potential for ambiguous cases.

Video Resource

Sine Rule Algebra 2

Kevinmathscience

Duration: 13:06
Watch on YouTube

Key Concepts

  • Sine Rule Formula (a/sinA = b/sinB)
  • Opposite sides and angles in a triangle
  • Cross-multiplication for solving proportions
  • Ambiguous Case of the Sine Rule (checking for two possible solutions when finding angles)

Learning Objectives

  • Students will be able to apply the Sine Rule to solve for unknown sides in non-right triangles.
  • Students will be able to apply the Sine Rule to solve for unknown angles in non-right triangles.
  • Students will be able to identify and solve problems involving the ambiguous case of the Sine Rule.

Educator Instructions

  • Introduction (5 mins)
    Briefly review trigonometric ratios (SOH CAH TOA) and their limitations to right triangles. Introduce the Sine Rule as a method for solving non-right triangles. Show the video introduction.
  • Video Explanation (10 mins)
    Play the Kevinmathscience video 'Sine Rule Algebra 2'. Students should take notes on the formula, the relationship between sides and angles, and the cross-multiplication method.
  • Worked Examples (15 mins)
    Work through examples similar to those in the video, emphasizing the steps involved in applying the Sine Rule, solving for sides, solving for angles, and checking for the ambiguous case.
  • Practice Problems (15 mins)
    Students work independently or in pairs on practice problems. Circulate to provide assistance and answer questions.
  • Review and Conclusion (5 mins)
    Review key concepts and address any remaining questions. Briefly introduce the Cosine Rule as a related concept for future learning.

Interactive Exercises

  • Triangle Solver Applet
    Use an online triangle solver applet to verify answers and explore different triangle configurations.
  • Real-World Application Problem
    Pose a problem involving surveying or navigation that requires the use of the Sine Rule to find distances or angles.

Discussion Questions

  • When can you use the Sine Rule to solve a triangle?
  • What does it mean for a triangle problem to have two solutions when using the Sine Rule?
  • Why is it important to check for a second possible angle when using the Sine Rule to find angles?

Skills Developed

  • Problem-solving
  • Algebraic manipulation
  • Trigonometric reasoning

Multiple Choice Questions

Question 1:

The Sine Rule states that a/sinA = b/sinB. What do 'a' and 'b' represent?

Correct Answer: Sides

Question 2:

When solving for an angle using the Sine Rule, why is it important to check for a second possible solution?

Correct Answer: Due to the ambiguous case where two triangles can satisfy the given conditions

Question 3:

If you have two angles and one side (AAS) of a triangle, can you use the Sine Rule to find the other sides?

Correct Answer: Yes

Question 4:

In triangle ABC, angle A = 30°, side a = 5, and angle B = 70°. Find side b.

Correct Answer: 9.04

Question 5:

What is the first step in solving for a missing side using the Sine Rule?

Correct Answer: Set up the proportion with known values

Question 6:

The sine rule cannot be used to solve which type of triangle?

Correct Answer: Right

Question 7:

Which of the following situations could have two possible triangle solutions? (SSA)

Correct Answer: Angle of 30 degrees, side 3 opposite, side 6 adjacent

Question 8:

When solving for a side length using the law of sines, do you have to check for alternate solutions?

Correct Answer: no

Question 9:

What formula do you use to find the third angle in a triangle when you know two?

Correct Answer: A+B+C=180

Question 10:

When can you not use the law of sines?

Correct Answer: SSS

Fill in the Blank Questions

Question 1:

The Sine Rule is useful for solving __________ triangles.

Correct Answer: non-right

Question 2:

In the Sine Rule formula a/sinA = b/sinB, 'A' and 'B' represent __________.

Correct Answer: angles

Question 3:

To solve a proportion created by the Sine Rule, you can use __________.

Correct Answer: cross-multiplication

Question 4:

When solving for angles using the Sine Rule, the ambiguous case may result in __________ possible solutions.

Correct Answer: two

Question 5:

If angle A=50 and angle B = 60, angle C = ____________

Correct Answer: 70

Question 6:

If side a = 10, sinA = .5, and sinB = .75, side B= ____________

Correct Answer: 15

Question 7:

If you do not have a matching side and angle, the law of _____ can not be used.

Correct Answer: sines

Question 8:

When you have SSA, this means you know two sides and an _____.

Correct Answer: angle

Question 9:

The angles of a triangle always add to _____ degrees.

Correct Answer: 180

Question 10:

a/sinA=b/sinB is the formula for the law of _____.

Correct Answer: sines

Educational Standards

A2.A.1:Represent and solve mathematical and real-world problems using nonlinear equations, systems of linear equations, and systems of linear inequalities; interpret the solutions in the original context. A2.A.2:Generate and evaluate equivalent algebraic expressions and equations using various strategies.

Teaching Materials

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