Unit Week Day CCSS Standards Objective I Can Statements Unit 6 Right Triangle Relationships and Trigonometry Week 18 – Indirect Measurements 86 CCSS.MATH.CONTENT.HSG.SRT.C.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. Identify opposite, adjacent and hypotenuse of right triangles. Define trigonometric ratios. I can Identify opposite, adjacent and hypotenuse of right triangles I can define trigonometric ratios. Unit 6 Right Triangle Relationships and Trigonometry Week 18 – Indirect Measurements 87 CCSS.MATH.CONTENT.HSG.SRT.C.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. Find trigonometric ratios of angles I can find trigonometric ratios of angles Unit 6 Right Triangle Relationships and Trigonometry Week 18 – Indirect Measurements 88 CCSS.MATH.CONTENT.HSG.SRT.C.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. Define trigonometric ratios of compliments. I can define trigonometric ratios of compliments. Unit 6 Right Triangle Relationships and Trigonometry Week 18 – Indirect Measurements 89 CCSS.MATH.CONTENT.HSG.SRT.C.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. Use similarity to find the trigonometric ratios of triangles with common angles. I can use similarity to find the trigonometric ratios of triangles with common angles.
Unit 6 Right Triangle Relationships and Trigonometry Week 18 – Indirect Measurements 90 Assessment Assessment Assessment Unit 6 Right Triangle Relationships and Trigonometry Week 19 – Trigonometric Ratios 91 CCSS.MATH.CONTENT.HSG.SRT.C.7 Explain and use the relationship between the sine and cosine of complementary angles. Explain the relationship between sine and cosine of complementary angles I can explain the relationship between sine and cosine of complementary angles Unit 6 Right Triangle Relationships and Trigonometry Week 19 – Trigonometric Ratios 92 CCSS.MATH.CONTENT.HSG.SRT.C.7 Explain and use the relationship between the sine and cosine of complementary angles. Use the relationship between the sine and cosine of complementary angles to solve geometric problems I can use the relationship between the sine and cosine of complementary angles to solve geometric problems Unit 6 Right Triangle Relationships and Trigonometry Week 19 – Trigonometric Ratios 93 CCSS.MATH.CONTENT.HSG.SRT.C.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.* Use trigonometric ratios to solve a triangle I can use trigonometric ratios to solve a triangle Unit 6 Right Triangle Relationships and Trigonometry Week 19 – Trigonometric Ratios 94 CCSS.MATH.CONTENT.HSG.SRT.C.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.* Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in word problems I can use trigonometric ratios and the Pythagorean Theorem to solve right triangles in word problems
Unit: Unit 6 Right Triangle Relationships and Trigonometry Course: Geometry Topic: Week 18 – Indirect Measurements Day: 87 Common Core State Standard: CCSS.MATH.CONTENT.HSG.SRT.C.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. Mathematical Practice: CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively Objective: Find trigonometric ratios of angles I can statement: I can find trigonometric ratios of angles Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 3. They will draw a right angle and verify the trigonometric ratios 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day. Materials: Bellringer 87 Day 87 Activities Day 87 Practice Day 87 Presentation Day 87 Exit Slip Accommodations/Special Circumstances: Technology:
Accommodations/Special Circumstances: Technology: Reflection: Extra/Additional Resources: Unit: Unit 6 Right Triangle Relationships and Trigonometry Course: Geometry Topic: Week 18 – Indirect Measurements Day: 90 Common Core State Standard: Assessment Mathematical Practice: Assessment Objective: Assessment I can statement: Assessment
Procedures: Assessment Materials: Assessment Accommodations/Special Circumstances: Technology: Reflection: Extra/Additional Resources: Unit: Unit 6 Right Triangle Relationships and Trigonometry Course: Geometry Topic: Week 19 – Trigonometric Ratios Day: 91 Common Core State Standard: CCSS.MATH.CONTENT.HSG.SRT.C.7 Explain and use the relationship between the sine and cosine of complementary angles. Mathematical Practice: CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others.
Unit: Unit 6 Right Triangle Relationships and Trigonometry Course: Geometry Topic: Week 19 – Trigonometric Ratios Day: 93 Common Core State Standard: CCSS.MATH.CONTENT.HSG.SRT.C.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.* Mathematical Practice: CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them. Objective: Use trigonometric ratios to solve a triangle I can statement: I can use trigonometric ratios to solve a triangle Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day. Materials: Bellringer 93 Day 93 Activities Day 93 Practice Day 93 Presentation Day 93 Exit Slip Accommodations/Special Circumstances: Technology:
Unit: Unit 6 Right Triangle Relationships and Trigonometry Course: Geometry Topic: Week 19 – Trigonometric Ratios Day: 95 Common Core State Standard: Assessment Mathematical Practice: Assessment Objective: Assessment I can statement: Assessment Procedures: Assessment Materials: Assessment Accommodations/Special Circumstances: Technology: Reflection: Extra/Additional Resources:
Unit: Unit 6 Right Triangle Relationships and Trigonometry Course: Geometry Topic: Week 20 – Special Right Triangles Day: 97 Common Core State Standard: CCSS.MATH.CONTENT.HSG.SRT.C.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. Mathematical Practice: CCSS.MATH.PRACTICE.MP1. Make sense of problems and persevere in solving them. CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically. Objective: Solve 30-60-90 right triangle I can statement: I can solve 30-60-90 right triangle Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day. Materials: Bellringer 97 Day 97 Activities Day 97 Practice Day 97 Presentation Day 97 Exit Slip Accommodations/Special Circumstances: Technology:
Unit: Unit 6 Right Triangle Relationships and Trigonometry Course: Geometry Topic: Week 20 – Special Right Triangles Day: 98 Common Core State Standard: CCSS.MATH.CONTENT.HSG.SRT.C.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. Mathematical Practice: CCSS.MATH.PRACTICE.MP1. Make sense of problems and persevere in solving them. CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically. Objective: Find the trigonometric ratios of 45-45-90 right triangle I can statement: I can find the trigonometric ratios of 45-45-90 right triangle Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day. Materials: Bellringer 98 Day 98 Activities Day 98 Practice Day 98 Presentation Day 98 Exit Slip Accommodations/Special Circumstances: Technology:
Unit: Unit 6 Right Triangle Relationships and Trigonometry Course: Geometry Topic: Week 20 – Special Right Triangles Day: 99 Common Core State Standard: CCSS.MATH.CONTENT.HSG.SRT.C.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. Mathematical Practice: CCSS.MATH.PRACTICE.MP1. Make sense of problems and persevere in solving them. CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically. Objective: Solve 45-45-90 right triangle I can statement: I can solve 45-45-90 right triangle Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day. Materials: Bellringer 99 Day 99 Activities Day 99 Practice Day 99 Presentation Day 99 Exit Slip Accommodations/Special Circumstances: Technology:
Reflection: Extra/Additional Resources: Unit: Unit 6 Right Triangle Relationships and Trigonometry Course: Geometry Topic: Week 20 – Special Right Triangles Day: 100 Common Core State Standard: Assessment Mathematical Practice: Assessment Objective: Assessment I can statement: Assessment Procedures: Assessment Materials: Assessment
Accommodations/Special Circumstances: Technology: Reflection: Extra/Additional Resources: Unit: Unit 6 Right Triangle Relationships and Trigonometry Course: Geometry Topic: Week 21 – Modeling with Right Triangles Day: 101 Common Core State Standard: CCSS.MATH.CONTENT.HSG.SRT.D.9 (+) Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. Mathematical Practice: CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively Objective: Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. I can statement: I can derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex
Unit: Unit 6 Right Triangle Relationships and Trigonometry Course: Geometry Topic: Week 21 – Modeling with Right Triangles Day: 102 Common Core State Standard: CCSS.MATH.CONTENT.HSG.SRT.D.10 (+) Prove the Laws of Sines and Cosines and use them to solve problems. Mathematical Practice: CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively Objective: Derive and apply sine rules I can statement: I can derive and apply sine rules Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day. Materials: Bellringer 102 Day 102 Activities Day 102 Practice Day 102 Presentation Day 102 Exit Slip Accommodations/Special Circumstances: Technology:
Unit: Unit 6 Right Triangle Relationships and Trigonometry Course: Geometry Topic: Week 21 – Modeling with Right Triangles Day: 103 Common Core State Standard: CCSS.MATH.CONTENT.HSG.SRT.D.10 (+) Prove the Laws of Sines and Cosines and use them to solve problems. Mathematical Practice: CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively Objective: Derive and apply cosine rules I can statement: I can derive and apply cosine rules Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day. Materials: Bellringer 103 Day 103 Activities Day 103 Practice Day 103 Presentation Day 103 Exit Slip Accommodations/Special Circumstances: Technology:
Unit: Unit 6 Right Triangle Relationships and Trigonometry Course: Geometry Topic: Week 21 – Modeling with Right Triangles Day: 104 Common Core State Standard: CCSS.MATH.CONTENT.HSG.SRT.D.11 (+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces). Mathematical Practice: CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively. CCSS.MATH.PRACTICE.MP8 Look for and express regularity in repeated reasoning. Objective: Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces). I can statement: I Understand and can apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces). Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day. Materials: Bellringer 104 Day 104 Activities Day 104 Practice Day 104 Presentation Day 104 Exit Slip
Accommodations/Special Circumstances: Technology: Reflection: Extra/Additional Resources: Unit: Unit 6 Right Triangle Relationships and Trigonometry Course: Geometry Topic: Week 21 – Modeling with Right Triangles Day: 105 Common Core State Standard: Assessment Mathematical Practice: Assessment Objective: Assessment I can statement: Assessment
6. Compare the expressions for the sines, cosines and tangents of the two angles. State whether the expressions are similar or different for each trigonometric ratio of the each of the two angles. In this activity, students will work in groups of four to compare trigonometric ratios of two complementary angles. The students in the groups will be equipped with a protractor, and a copy of right labeled such that is the right angle, and . The sides should be labelled as shown. Answer keys Day 88: 1. 2. 3. The sum is ; Complementary angles 4. 5. 6. The expressions are different for each trigonometric ratio of each angle.
Answer keys Day 88: 1. 2. and are complements to each other/ they are complementary angles 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. Use right to answer the questions that follow.
Day 89: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. In the diagram below, and . Calculate the tangent of Answer Keys Day 89: 1.
1. Measure the length of the wooden pole using the surveyor’s tape measure provided. 2. Record the length of the pole in the writing pad provided. 3. Let one member of your group hold the pole upright ensuring that the flat surface is properly aligned to the ground. 4. Measure the length of the shadow formed by the pole using the tape measure. 5. Record the length of this shadow in the writing pad provided. 6. Record the time at the moment you are measuring the length of the shadow. 7. The sketch below represents a right triangle to depict the position of the pole and the shadow. It will guide you in calculating the angle of elevation of the sun, . 8. Using as the reference angle, which side of the right triangle is represented by the length of the wooden pole?
a) Find its area. b) Find the value of a) Find the value of b) Find the area of the triangle. 3. The three sides of a triangular plot measures and. a) Find the angle between the shortest and the longest side. b) Find its area. 4. Use the figure below to answer the questions that follow. a) Find the length of DB. b) Find the length of BC. 5. The longest side and the shortest side of a right triangle measures and respectively. a) Find the angle between the shortest and the longest side. b) Find the length of the third side. 6. One short side of a right triangle has a length of and its makes with the longest side. a) Find the length of the longest side. b) Find the length of the other shorter side.