Curriculum / Math / 10th Grade / Unit 4: Right Triangles and Trigonometry / Lesson 17
Math
Unit 4
10th Grade
Lesson 17 of 19
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Verify algebraically and find missing measures using the Law of Sines.
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 foundational standards covered in this lesson
7.RP.A.2 — Recognize and represent proportional relationships between quantities.
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 #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.Â
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
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..
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.
In $${\triangle ABC}$$, $${a=9}$$, $${c=12}$$, and $${\angle A=30^\circ}$$. Determine the missing angle and side measurements.
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 the 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 16
Lesson 18
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
G.SRT.D.10
Verify algebraically and find missing measures using the Law of Cosines.
Use side and angle relationships in right and non-right triangles to solve application problems.
G.SRT.D.11
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