Verify algebraically and find missing measures using the Law of Sines.
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Anchor Problem #2 will require the teacher to do a significant amount of modeling to define and algebraically verify the Law of Sines. Reference EngageNY, Geometry, Module 2, Lesson 32: Teacher Version (Discussion) for more guidance on this.
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a. Find the lengths of $$d$$ and $$e$$.
b. Why can't you use the same method to find the lengths of $$x$$ and $$y$$?
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 The Match Foundation, Inc.There is a rule, the Law of Sines, which allows you to use trigonometric ratios to determine side lengths and angles of non-right triangles.
Law of Sines:
Given $${\triangle ABC}$$,
Using the two congruent triangles below and the altitudes drawn, show that the Law of Sines is true.
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..
In $${\triangle ABC}$$, $${a=9}$$, $${c=12}$$, and $${\angle A=30^\circ}$$. Determine the missing angle and side measurements.
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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.
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Use the Law of Sines to find the lengths $$b$$ and $$c$$ in the triangle below. Round answers to the nearest tenth as necessary.
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..