CCGPS Mathematics Unit-by-Unit Grade Level Webinar Accelerated Coordinate Algebra/Analytic Geometry A Unit 8: Right Triangle Trigonometry November 15, 2012 Session will be begin at 8:00 am While you are waiting, please do the following: Configure your microphone and speakers by going to: Tools – Audio – Audio setup wizard Document downloads: When you are prompted to download a document, please choose or create the folder to which the document should be saved, so that you may retrieve it later.

CCGPS Mathematics Unit-by-Unit Grade Level Webinar Accelerated Coordinate Algebra/Analytic Geometry A Unit 8: Right Triangle Trigonometry November 15, 2012 James Pratt – Brooke Kline – Secondary Mathematics Specialists These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.

Expectations and clearing up confusion Intent and focus of Unit 8 webinar. Framework tasks. GPB sessions on Georgiastandards.org. Standards for Mathematical Practice. Resources. CCGPS is taught and assessed from and beyond.

The big idea of Unit 8 Incorporating SMPs into right triangle trigonometry Resources Welcome!

Feedback James Pratt – Brooke Kline – Secondary Mathematics Specialists

Bivariate or two-way frequency chart  Joint frequencies  Marginal frequencies  Relative joint frequencies  Relative marginal frequencies  Conditional frequencies Wiki/ Questions

 Question: Are we supposed to teach special right triangles? I only see this topic as a couple of small tasks, but it is not stated in the standards. Wiki/ Questions

 Question: Are we not teaching the tangent ratio anymore? I only see reference to sine and cosine in the standards and tasks.  Question: Which trig ratios are we supposed to teach: Sine, Cosine, Tangent, Secant, Cosecant & Cotangent or just Sine, Cosine & Tangent? MCC9-12.G.SRT.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. MCC9-12.G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles. Wiki/ Questions

 Question: Didn't students solve Pythagorean Theorem applied problems when they learned the Pythagorean Theorem? 8 th Grade: MCC8.G.6 Explain a proof of the Pythagorean Theorem and its converse. MCC8.G.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real- world and mathematical problems in two and three dimensions. MCC8.G.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. Coordinate Algebra: MCC9-12.G.GPE.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. Analytic Geometry MCC9-12.G.SRT.4 Prove theorems about triangles…; the Pythagorean Theorem proved using triangle similarity. MCC9-12.G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. Wiki/ Questions

If four circles are placed around a central circle with diameter of 6 cm, as pictured below, what is the radius length of each of the outer circles? Adapted from Illustrative Mathematics G.SRT Seven Circle III 6 cm

Tiered Exit Cards

What’s the big idea? Using similar triangles to develop understanding of trigonometric ratios. Determine that trigonometric ratios can be used to solve application problems involving right triangles. Standards for Mathematical Practice.

Coherence and Focus K-8 th  Identifying right triangles  Ratios and proportional reasoning  Pythagorean Theorem  Similarity 10 th -12 th  Trigonometric functions  Trigonometry in general triangles

Examples & Explanations Adapted from Right Triangle Trigonometry, and Trigonometric Functions: Doris Santarone

Examples & Explanations Adapted from Right Triangle Trigonometry, and Trigonometric Functions: Doris Santarone

Examples & Explanations Adapted from Right Triangle Trigonometry, and Trigonometric Functions: Doris Santarone 37° C”C” B”B” A”A”

Examples & Explanations What did you notice between the three similar triangles? Adapted from Right Triangle Trigonometry, and Trigonometric Functions: Doris Santarone 37° C B A C’C’ B’B’ A’A’ 37° C”C” B”B” A”A”

Examples & Explanations Adapted from Right Triangle Trigonometry, and Trigonometric Functions: Doris Santarone

Examples & Explanations Adapted from Right Triangle Trigonometry, and Trigonometric Functions: Doris Santarone

Examples & Explanations A 25-foot flag pole is erected on the top of a building 10 feet from the side. The guide wire must be anchored to the adjacent building 15 feet away and two feet from the top of the pole. The wire is at a 50° angle with the horizon. How long does the wire need to be?

Examples & Explanations A 25-foot flag pole is erected on the top of a building 10 feet from the side. The guide wire must be anchored to the adjacent building 15 feet away and two feet from the top of the pole. The wire is at a 50° angle with the horizon. How long does the wire need to be?

Examples & Explanations A 25-foot flag pole is erected on the top of a building 10 feet from the side. The guide wire must be anchored to the adjacent building 15 feet away and two feet from the top of the pole. The wire is at a 50° angle with the horizon. How long does the wire need to be? 15 ft 25 ft 10 ft 2 ft 50°

Examples & Explanations A 25-foot flag pole is erected on the top of a building 10 feet from the side. The guide wire must be anchored to the adjacent building 15 feet away and two feet from the top of the pole. The wire is at a 50° angle with the horizon. How long does the wire need to be? 15 ft 25 ft 10 ft 2 ft 50° 25 ft

Examples & Explanations A 25-foot flag pole is erected on the top of a building 10 feet from the side. The guide wire must be anchored to the adjacent building 15 feet away and two feet from the top of the pole. The wire is at a 50° angle with the horizon. How long does the wire need to be? 15 ft 25 ft 10 ft 2 ft 50° 25 ft

Examples & Explanations A 25-foot flag pole is erected on the top of a building 10 feet from the side. The guide wire must be anchored to the adjacent building 15 feet away and two feet from the top of the pole. The wire is at a 50° angle with the horizon. How long does the wire need to be? 15 ft 25 ft 10 ft 2 ft 50° 25 ft

Examples & Explanations A 25-foot flag pole is erected on the top of a building 10 feet from the side. The guide wire must be anchored to the adjacent building 15 feet away and two feet from the top of the pole. The wire is at a 50° angle with the horizon. How long does the wire need to be? 15 ft 25 ft 10 ft 2 ft 50° 25 ft

Examples & Explanations A 25-foot flag pole is erected on the top of a building 10 feet from the side. The guide wire must be anchored to the adjacent building 15 feet away and two feet from the top of the pole. The wire is at a 50° angle with the horizon. How long does the wire need to be? 15 ft 25 ft 10 ft 2 ft 50° 25 ft

Examples & Explanations Landing in a hot air balloon, you notice the landing spot and your car. From 100 ft. in the air, you have to look down at a 30° angle to your car and an additional 21° to the landing spot. How far will you have to walk to your car after landing?

Examples & Explanations Landing in a hot air balloon, you notice the landing spot and your car. From 100 ft. in the air, you have to look down at a 30° angle to your car and an additional 21° to the landing spot. How far will you have to walk to your car after landing? 100 ft

Examples & Explanations Landing in a hot air balloon, you notice the landing spot and your car. From 100 ft. in the air, you have to look down at a 30° angle to your car and an additional 21° to the landing spot. How far will you have to walk to your car after landing? 100 ft 30° 21°

Examples & Explanations Landing in a hot air balloon, you notice the landing spot and your car. From 100 ft. in the air, you have to look down at a 30° angle to your car and an additional 21° to the landing spot. How far will you have to walk to your car after landing? 100 ft 30° 21° 51°30°

Examples & Explanations Landing in a hot air balloon, you notice the landing spot and your car. From 100 ft. in the air, you have to look down at a 30° angle to your car and an additional 21° to the landing spot. How far will you have to walk to your car after landing? x 100 ft 30° 21° 51°30° y

x 100 ft 30° 21° 51°30° y Examples & Explanations

x 100 ft 30° 21° 51°30° y Examples & Explanations

x 100 ft 30° 21° 51°30° y Examples & Explanations

x 100 ft 30° 21° 51°30° y Examples & Explanations

x 100 ft 30° 21° 51°30° y Examples & Explanations

x 100 ft 30° 21° 51°30° y Examples & Explanations

x 100 ft 30° 21° 51°30° y Examples & Explanations

If four circles are placed around a central circle with diameter of 6 cm, as pictured below, what is the radius length of each of the outer circles? Adapted from Illustrative Mathematics G.SRT Seven Circle III 6 cm

If four circles are placed around a central circle with diameter of 6 cm, as pictured below, what is the radius length of each of the outer circles? Adapted from Illustrative Mathematics G.SRT Seven Circle III

If four circles are placed around a central circle with diameter of 6 cm, as pictured below, what is the radius length of each of the outer circles? Adapted from Illustrative Mathematics G.SRT Seven Circle III Q O R P

If four circles are placed around a central circle with diameter of 6 cm, as pictured below, what is the radius length of each of the outer circles? Adapted from Illustrative Mathematics G.SRT Seven Circle III Q O R P 3 3 t t t t

If four circles are placed around a central circle with diameter of 6 cm, as pictured below, what is the radius length of each of the outer circles? Adapted from Illustrative Mathematics G.SRT Seven Circle III Q O R P 3 3 t t t t 45°

Adapted from Illustrative Mathematics G.SRT Seven Circle III Q O R P 3 3 t t t t 45°

Adapted from Illustrative Mathematics G.SRT Seven Circle III Q O R P 3 3 t t t t 45°

Adapted from Illustrative Mathematics G.SRT Seven Circle III Q O R P 3 3 t t t t 45°

Adapted from Illustrative Mathematics G.SRT Seven Circle III Q O R P 3 3 t t t t 45°

Adapted from Illustrative Mathematics G.SRT Seven Circle III Q O R P 3 3 t t t t 45°

Adapted from Illustrative Mathematics G.SRT Seven Circle III Q O R P 3 3 t t t t 45°

Resource List The following list is provided as a sample of available resources and is for informational purposes only. It is your responsibility to investigate them to determine their value and appropriateness for your district. GaDOE does not endorse or recommend the purchase of or use of any particular resource.

Common Core Resources  SEDL videos - or  Illustrative Mathematics -  Dana Center's CCSS Toolbox -  Common Core Standards -  Tools for the Common Core Standards -  Phil Daro talks about the Common Core Mathematics Standards -  LearnZillion - Assessment Resources  MAP -  Illustrative Mathematics -  CCSS Toolbox: PARCC Prototyping Project -  PARCC -  Online Assessment System - Resources

Professional Learning Resources  Inside Mathematics-  Annenberg Learner -  Edutopia –  Teaching Channel -  Ontario Ministry of Education - Blogs  Dan Meyer –  Timon Piccini –  Dan Anderson – Unit Resource  Right Triangle Trigonometry, and Trigonometric Functions: Doris Santarone -

Thank You! Please visit to share your feedback, ask questions, and share your ideas and resources! Please visit to join the 9-12 Mathematics listserve. Follow on Twitter! Brooke Kline Program Specialist (6 ‐ 12) James Pratt Program Specialist (6-12) These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.