Geometry: Pythagorean Theorem and Triangle Types
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Geometry: Pythagorean Theorem and Triangle Types

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@CalmingCornet

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Questions and Answers

What is the Pythagorean Theorem used for?

  • To calculate the volume of a cube
  • To find the area of a triangle
  • To find the missing side of a right triangle (correct)
  • To find the circumference of a circle
  • If $c^2 = a^2 + b^2$, then the triangle is right.

    True

    If $c^2 < a^2 + b^2$, then the triangle is acute.

    True

    If $c^2 > a^2 + b^2$, then the triangle is obtuse.

    <p>True</p> Signup and view all the answers

    What are the side ratios of a 45-45-90 right triangle?

    <p>1 : 1 : Square root 2</p> Signup and view all the answers

    What are the side ratios of a 30-60-90 right triangle?

    <p>1 : Square root 3 : 2</p> Signup and view all the answers

    What is trigonometry?

    <p>The study of triangle measurements (side and angle).</p> Signup and view all the answers

    What is sine?

    <p>The ratio of the leg opposite the angle to the hypotenuse.</p> Signup and view all the answers

    What is cosine?

    <p>The ratio of the leg adjacent to the angle to the hypotenuse.</p> Signup and view all the answers

    What is tangent?

    <p>The ratio of the leg opposite the angle to the leg adjacent to the angle.</p> Signup and view all the answers

    Study Notes

    Pythagorean Theorem

    • Utilized to determine the missing side length in a right triangle.
    • Legs of the triangle are designated as A and B; C is the hypotenuse.
    • Formula: ( a^2 + b^2 = c^2 ).

    Identifying Triangle Types

    • Right Triangle: Occurs when ( c^2 = a^2 + b^2 ).
    • Acute Triangle: Characterized by ( c^2 < a^2 + b^2 ).
    • Obtuse Triangle: Identified when ( c^2 > a^2 + b^2 ).

    Special Right Triangles

    • 45 - 45 - 90 Triangle: Ratio of the sides is 1:1:( \sqrt{2} ).
    • 30 - 60 - 90 Triangle: Side length ratios are 1:( \sqrt{3} ):2.

    Trigonometry

    • Focuses on the measurements of triangles, including side lengths and angles.

    Trigonometric Ratios

    • Sine: Ratio of the length of the opposite side to the hypotenuse.
    • Cosine: Ratio of the length of the adjacent side to the hypotenuse.
    • Tangent: Ratio of the length of the opposite side to the adjacent side.

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    Description

    Test your understanding of the Pythagorean theorem, the different types of triangles, and special right triangles. This quiz explores trigonometric ratios and their applications in solving for side lengths and angles in triangles.

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