Right Triangles and Trigonometry

Lesson 18

Math

Unit 4

10th Grade

Lesson 18 of 19

Objective


Verify algebraically and find missing measures using the Law of Cosines.

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. Identify a situation where the law of sines is not an effective method to solving a triangle.
  2. Given the Law of Cosines describe the relationship to the Pythagorean theorem.
  3. Describe when you would use the Pythagorean theorem rather than the Law of Cosines to solve a right triangle.
  4. Verify the Law of Cosines algebraically and use this to solve triangles.
  5. Identify when to use the Law of Sines, Law of Cosines, or area formula in terms of sine to solve triangles or find missing measures. Find missing measures in non-right triangles in non-contextual problems.

Tips for Teachers


Anchor Problem #1 will require the teacher to do a significant amount of modeling to define and algebraically verify the Law of Cosines. Reference EngageNY, Geometry, Module 2, Lesson 32: Teacher Version for more guidance on this.

Fishtank Plus

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Anchor Problems

25-30 minutes


Problem 1

The Law of Cosines states that:

Given $${\triangle ABC}$$,

What measurements of a triangle make the most sense to use the Law of Cosines? 

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Problem 2

For each of the triangles below, would you use the Law of Sines, Law of Cosines, or Pythagorean theorem to find the value of $$x$$? Explain your reasoning

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

References

EngageNY Mathematics Geometry > Module 2 > Topic E > Lesson 33Opening Exercise

Geometry > Module 2 > Topic E > Lesson 33 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.

Target Task

5-10 minutes


Given $${\triangle DEF}$$, use the Law of Cosines to find the side length marked $$d$$ to the nearest tenth.

References

EngageNY Mathematics Geometry > Module 2 > Topic E > Lesson 33Exit Ticket, Question #1

Geometry > Module 2 > Topic E > Lesson 33 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.

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.

  • Include problems where students algebraically verify the Law of Cosines on their own.
  • Include problems where students need to determine whether using the Law of Sines, Law of Cosines, Pythagorean theorem, or area formulas would be the most efficient way to find the missing measurements.

Next

Use side and angle relationships in right and non-right triangles to solve application problems.

Lesson 19
icon/arrow/right/large

Lesson Map

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

Topic A: Right Triangle Properties and Side-Length Relationships

Topic B: Right Triangle Trigonometry

Topic C: Applications of Right Triangle Trigonometry

Topic D: The Unit Circle

Topic E: Trigonometric Ratios in Non-Right Triangles

Request a Demo

See all of the features of Fishtank in action and begin the conversation about adoption.

Learn more about Fishtank Learning School Adoption.

Contact Information

School Information

What courses are you interested in?

ELA

Math

Are you interested in onboarding professional learning for your teachers and instructional leaders?

Yes

No

Any other information you would like to provide about your school?

We Handle Materials So You Can Focus on Students

We Handle Materials So You Can Focus on Students

We've got you covered with rigorous, relevant, and adaptable math lesson plans for free