Trigonometric Identities and Equations

Lesson 15

Math

Unit 7

11th Grade

Lesson 15 of 16

Objective


Use the Law of Sines to find missing side lengths and angle measures in acute triangles.

Common Core Standards


Core Standards

  • G.SRT.D.10 — Prove the Laws of Sines and Cosines and use them to solve problems.

Criteria for Success


  1. Derive the Law of Sines.
  2. Identify when the Law of Sines can be applied to triangles.
  3. Apply the Law of Sines to find missing side lengths.
  4. Apply the Law of Sines to find missing angles.
  5. Apply the Law of Sines with word problems.

Tips for Teachers


Law of Sines -- Ambiguous Case by Karl Mealor is a great explanation of the ambiguous case with the Law of Sines. This is not emphasized in the current lesson but is a useful extension.

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Anchor Problems

25-30 minutes


Problem 1

Find the lengths of $$d$$ and $$e$$.

Why can't yo uuse the same method to find the lengths of $$x$$ and $$y$$ in the triangle below?

Guiding Questions

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References

EngageNY Mathematics Geometry > Module 2 > Topic E > Lesson 32Opening Exercise

Geometry > Module 2 > Topic E > Lesson 32 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

Problem 2

There is a rule that allows you to use trigonometric ratios to determine side lengths and angles of non-right triangles.

Law of Sines:

Using the two diagrams below and the altitudes drawn, show that this is true.

Guiding Questions

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Problem 3

A surveyor needs to determine the distance between two points $$A$$ and $$B$$ that lie on opposite banks of a river. A point $$C$$ is chosen $${160}$$ meters from point $$A$$, on the same side of the river as $$A$$. The measures of $$\angle BAC$$ and $$\angle ACB$$ are $${41^{\circ}}$$ and $${55^{\circ}}$$, respectively. Approximate the distance from $$A$$ to $$B$$ to the nearest meter.

Guiding Questions

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References

EngageNY Mathematics Geometry > Module 2 > Topic E > Lesson 32Example 1

Geometry > Module 2 > Topic E > Lesson 32 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Target Task

5-10 minutes


Use the Law of Sines to find lengths $$b$$ and $$c$$ in the triangle below. Round answers to the nearest tenth as necessary.

References

EngageNY Mathematics Geometry > Module 2 > Topic E > Lesson 32Exit Ticket, Question #1

Geometry > Module 2 > Topic E > Lesson 32 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Additional Practice


The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

  • Be sure to include an example that you highlight during independent practice that deals with the ambiguous case where a unique triangle is not given via the Law of Sines. This is a great way to review why Side-Side-Angle is not a congruence criterion.

Next

Find missing side lengths and angle measures using the Law of Cosines in acute triangles.

Lesson 16
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Basic Trigonometric Identities and Equivalent Expressions

Topic B: Solve Trigonometric Equations

Topic C: Advanced Identities and Solving Trigonometric Equations

Topic D: Applications and Extensions of Trigonometric Functions

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