Curriculum / Math / 10th Grade / Unit 4: Right Triangles and Trigonometry / Lesson 18
Math
Unit 4
10th Grade
Lesson 18 of 19
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Verify algebraically and find missing measures using the Law of Cosines.
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
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.
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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 that:
Given $${\triangle ABC}$$,
What measurements of a triangle make the most sense to use the Law of Cosines?
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
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
Given $${\triangle DEF}$$, use the Law of Cosines to find the side length marked $$d$$ to the nearest tenth.
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 17
Lesson 19
Topic A: Right Triangle Properties and Side-Length Relationships
Define the parts of a right triangle and describe the properties of an altitude of a right triangle.
G.CO.A.1 G.SRT.B.4
Define and prove the Pythagorean theorem. Use the Pythagorean theorem and its converse in the solution of problems.
G.SRT.B.4
Define the relationship between side lengths of special right triangles.
G.SRT.B.4 G.SRT.B.5
Multiply and divide radicals. Rationalize the denominator.
A.SSE.A.2 N.RN.A.2
Add and subtract radicals.
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Topic B: Right Triangle Trigonometry
Define and calculate the sine of angles in right triangles. Use similarity criteria to generalize the definition of sine to all angles of the same measure.
G.SRT.C.6
Define and calculate the cosine of angles in right triangles. Use similarity criteria to generalize the definition of cosine to all angles of the same measure.
Derive the relationship between sine and cosine of complementary angles in right triangles, and describe sine and cosine as angle measures approach 0°, 30°, 45°, 60°, and 90°.Â
G.SRT.C.7
Describe and calculate tangent in right triangles. Describe how the value of tangent changes as the angle measure approaches 0°, 45°, and 90°.
G.SRT.C.6 G.SRT.C.7
Solve for missing sides of a right triangle given the length of one side and measure of one angle.
G.SRT.C.8
Topic C: Applications of Right Triangle Trigonometry
Find the angle measure given two sides using inverse trigonometric functions.
Describe the relationship between slope and the tangent ratio of the angle of elevation/depression. Use the tangent ratio of the angle of elevation or depression to solve real-world problems.
Solve a modeling problem using trigonometry.
Topic D: The Unit Circle
Define angles in standard position and use them to build the first quadrant of the unit circle.
F.TF.A.2
Use the first quadrant of the unit circle to define sine, cosine, and tangent values outside the first quadrant.
Topic E: Trigonometric Ratios in Non-Right Triangles
Derive the area formula for any triangle in terms of sine.
G.SRT.D.9
Verify algebraically and find missing measures using the Law of Sines.
G.SRT.D.10
Use side and angle relationships in right and non-right triangles to solve application problems.
G.SRT.D.11
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