Curriculum / Math / 11th Grade / Unit 7: Trigonometric Identities and Equations / Lesson 15
Math
Unit 7
11th Grade
Lesson 15 of 16
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Use the Law of Sines to find missing side lengths and angle measures in acute triangles.
The core standards covered in this lesson
G.SRT.D.10 — Prove the Laws of Sines and Cosines and use them to solve problems.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
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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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
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?
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..
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.
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.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Use the Law of Sines to find lengths $$b$$ and $$c$$ in the triangle below. Round answers to the nearest tenth as necessary.
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.
Lesson 14
Lesson 16
Topic A: Basic Trigonometric Identities and Equivalent Expressions
Derive and verify trigonometric identities using transformations and equivalence of functions.
F.TF.C.8
Derive and use the Pythagorean identity to write equivalent expressions.
Verify trigonometric identities using Pythagorean and reciprocal identities.
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Topic B: Solve Trigonometric Equations
Find angle measures using inverse trig functions in right triangles.
F.TF.B.6 F.TF.B.7
Analyze inverse trigonometric functions graphically.
F.BF.B.4.D F.IF.C.7.E F.TF.B.6 F.TF.B.7
Solve linear trigonometric equations.
F.TF.B.7
Solve linear trigonometric equations using $$u$$-substitution.
Use inverse trigonometric functions to solve contextual problems.
Solve quadratic trigonometric equations.
Solve trigonometric equations using identities.
F.TF.B.7 F.TF.C.8
Topic C: Advanced Identities and Solving Trigonometric Equations
Evaluate expressions using sum and difference formulas.
F.TF.C.9
Solve equations and prove identities using sum and difference formulas.
Derive double angle formulas and use them to solve equations and prove identities.
Use trigonometric identities to analyze graphs of functions.
F.TF.C.8 F.TF.C.9
Topic D: Applications and Extensions of Trigonometric Functions
G.SRT.D.10
Find missing side lengths and angle measures using the Law of Cosines in acute triangles.
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