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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
Standard:
G-SRT.7
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.
G-SRT.8
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 non-right
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/
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