Right Triangle Trigonometry

8 Components
Initial Task
Hopewell Geometry
Big Ideas
Big Idea 1 Big Idea 2
Formative Assessment Lesson
Proofs of the Pythagorean Theorem
Re-engagement
Re-engagement for Unit 4
End of Unit Assessments
End of Unit Assessment for Unit 4 End of Unit Assessment Teacher Resources for GEO Unit 4 Find aligned Regents questions with Quiz Banker
Geo U4: Right Triangle Trigonometry
Browse Components
Initial Task
Hopewell Geometry
Big Ideas
Big Idea 1 Big Idea 2
Formative Assessment Lesson
Proofs of the Pythagorean Theorem
Re-engagement
Re-engagement for Unit 4
End of Unit Assessments
End of Unit Assessment for Unit 4 End of Unit Assessment Teacher Resources for GEO Unit 4 Find aligned Regents questions with Quiz Banker
Big Idea:

Big Idea 2

Sine, Cosine, and Tangent are constant ratios that relate the angles and sides of a right triangle.

1 week
See Standards
Common Core: Major Standards:
G-SRT.C.6

Define trigonometric ratios and solve problems involving right triangles. 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.

G-SRT.C.7

Define trigonometric ratios and solve problems involving right triangles. Explain and use the relationship between the sine and cosine of complementary angles.

G-SRT.C.8

Define trigonometric ratios and solve problems involving right triangles. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.★

Common Core: Additional Standards:
G-GMD.A.1

Explain volume formulas and use them to solve problems. Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. (e.g. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.)

G-GMD.A.3

Explain volume formulas and use them to solve problems. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.★

Evidence of Understanding

  • analyze characteristics of trigonometric ratios using right triangles
    • use similarity, dilations, and scale factor to justify why a trigonometric ratio is constant
    • analyze the legs of a right triangle to describe sine and cosine
      • use the definition of the sine or cosine ratio to explain why neither value can exceed 1
      • describe how increasing or decreasing one leg impacts the sine or cosine value
      • explain how the sine and cosine of complementary angles are related and create an algebraic expression that generalizes the relationship between sine and cosine
    • analyze the legs of a right triangle to describe the tangent
      • use the definition of the tangent ratio to explain why the tangent values increases without limit as the angle increases
      • describe features of a right triangle whose tangent is 1 (isosceles, 45-45-90)
      • explain why the tangent of 45° is always 1
    • use examples and nonexamples to make conjectures about special right triangles
      • the short side of a 30-60-90 triangle is always half the length of the hypotenuse
      • the sine of 30° is always ½ and, conversely,  if the sine is ½ then the angle is 30°
      • the cosine of 60° is always ½ and, conversely,  if the cosine is ½ then the angle is 60°
  • determine the measure of angles or sides using right triangles and trigonometric ratios
    • determine when to use Pythagorean Theorem or trig ratios (or a combination of methods) to solve right triangles
      • create diagrams and write equations to model situations using right triangles
      • recognize Pythagorean Theorem cannot be used to determine an unknown angle
    • find the value of an unknown angle using inverse trig functions (sin-1, cos-1, and tan-1)
      • determine the angle of depression or angle of elevation
    • use special triangle patterns (30-60-90 and 45-45-90) to determine a missing measure
    • find the area or perimeter of a simple polygon with right triangles using a variety of methods including trig, Pythagorean Theorem, special triangles, etc.

Develop conceptual understanding:

trigonometric ratios, sine, cosine, tangent, special right triangle, inverse trig, angle of depression, angle of elevation

Supporting terms to communicate:

constant ratio, similarity, scale factor, leg, side, opposite, adjacent, hypotenuse, corresponding, complementary, isosceles triangle
Core Resource
A core resource supports multiple days of instruction.
  • Introducing Right Triangles
    This single-day resource motivates the need for right-angle trigonometry.
    Resource:
    Introducing Right Triangles

    Geometry & Algebra II Archive

    Geo U4: Right Triangle Trigonometry

    Big Idea: Big Idea 2

    The objective for this initial introduction is to motivate the use of right-angle trigonometry through an investigation followed by a problem solving task using the results of that investigation.

    Preview ResourceAdd a Copy of Resource to my Google Drive
    Type
    Geometry: Right Triangle Trigonometry
    File
    Google Doc
    Tags
    activity
    Standards
    Common Core: Major Standards ( G-SRT.C.6, G-SRT.C.7, G-SRT.C.8 ) Common Core: A…
    +— Details
    Common Core: Major Standards:
    G-SRT.C.6

    Define trigonometric ratios and solve problems involving right triangles. 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.

    G-SRT.C.7

    Define trigonometric ratios and solve problems involving right triangles. Explain and use the relationship between the sine and cosine of complementary angles.

    G-SRT.C.8

    Define trigonometric ratios and solve problems involving right triangles. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.★

    Common Core: Additional Standards:
    G-GMD.A.1

    Explain volume formulas and use them to solve problems. Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. (e.g. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.)

    G-GMD.A.3

    Explain volume formulas and use them to solve problems. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.★

    All Resources From: