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Progressive Mathematics Initiative www.njctl.org Mathematics Curriculum Unit Plan # 7 Title: Trigonometry of Right Triangles Subject: Geometry Length of Time: 3 weeks Unit Summary: The unit is an introduction to trigonometry. The unit begins with the ratios of 30-60-90 and 45-45-90 and solving problems with those ratios. These special right triangles lead into the sine, cosine, and tangent ratios. The unit concludes with solving problems using laws of cosine and sine Learning Targets Conceptual Category: Geometry Domain: Similarity, Right Triangles, and Trigonometry Cluster: Define trigonometric ratios and solve problems involving right Triangles Standard#: G-SRT.6 G-SRT.7 G-SRT.8 Standard: 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. Explain and use the relationship between the sine and cosine of complementary angles. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. Cluster: Apply trigonometry to general triangles Standard#: G-SRT.9 G-SRT.10 G-SRT.11 Standard: 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. Prove the Laws of Sines and Cosines and use them to solve problems. Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and nonright triangles (e.g., surveying problems, resultant forces). Unit Essential Question: What is the relationship between the sides and angles of right triangles? Unit Enduring Understandings: Geometric mean Pythagorean Theorem Sine, Cosine, and Tangent Law of Sines Law of Cosines Area of a Triangle Unit Objectives: Students will be able to solve problems and identify right triangles using Pythagorean Theorem Students will be able to use trigonometric ratios to solve right triangles Students will be able to solve triangles using Law of Sines and Law of Cosines Students will be able to find the area of an oblique triangle Students will be able to derive the trigonometry formulas Evidence of Learning Formative Assessments: SMART Response questions used throughout the unit. 5 Quizzes 1 Lab Summative Assessment: Unit Test Lesson Plan Topics Topic #1: Pythagorean Theorem Quiz#1: Pythagorean Theorem and Pythagorean Theorem Converse Topic #2: Similarity in Right Triangles Lab #1: Similar Right Triangles Quiz#2: Similarity in Right Triangles Topic #3: Special Right Triangle Quiz #3: Special Right Triangles Topic #4: Trigonometric Ratios Lab #2: Finding Trigonometric Ratios Topic #5: Solving Right Triangles Topic #6: Angles of Elevation and Depression Lab #3: Height of a Tree Quiz #4: Trig Ratios and Solving Right Triangles Topic #7: Law of Sines & Law of Cosines Topic #8: Area of an Oblique Triangle Quiz #5: Law of Sines & Law of Cosines and Area of an Oblique Triangle Topic #9: Review and Unit Test Curriculum Resources: www.njctl.org/courses/math/geometry/ 1 1 2 2 2 1 2 1 3