Curriculum / Math / 11th Grade / Unit 7: Trigonometric Identities and Equations / Lesson 16
Math
Unit 7
11th Grade
Lesson 16 of 16
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Find missing side lengths and angle measures using the Law of Cosines 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
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
The Law of Cosines states:
What measurements of a traingle make the most sense to use the Law of Cosines?
Would you use Law of Sines, Law of Cosines, or Pythagoream Theorem to find the value of $$x$$?
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..
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Use the Law of Cosines to find the solution to the following problem.
Your school is challenging classes to compete in a triathlon. The race begins with a swim along the shore and then continues with a bike ride for $$4$$ miles. School officials want the race to end at the place it began, so after the $$4$$-mile bike ride, racers must turn $${30^{\circ}}$$ and run $${3.5}$$ miles directly back to the starting point. What is the total length of the race? Round your answers to the tenths place.
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 15
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
Use the Law of Sines to find missing side lengths and angle measures in acute triangles.
G.SRT.D.10
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