## Class Details

- Class Name:
- Trigonometry: The Pythagorean Theorem 201
- Difficulty:
- Intermediate
- Number of Lessons:
- 15

## Class Outline

- Right Triangles
- The Pythagorean Theorem
- Powers and Roots
- Solving for an Unknown Hypotenuse
- Solving for an Unknown Leg
- Pythagorean Theorem Review
- Circle in a V-Block
- Circle in a V-Block
- Solving for an Unknown Dimension of Irregular Object
- Solving for an Unknown Dimension of an Irregular Object
- Solving for Missing Dimensions Review
- Die Punch Sample Problem
- Die Punch Sample Problem
- Die Punch Sample Problem
- Die Punch Problem Review

## Objectives

- Describe the characteristics of a right triangle.
- Explain the Pythagorean theorem.
- Describe the different trigonometric elements of using the Pythagorean theorem.
- Solve for the unknown hypotenuse of a right triangle using the Pythagorean theorem.
- Solve for an unknown leg of a right triangle.
- Describe how tangents and right triangles are used to find an unknown dimension on an irregular form.
- Solve for a missing dimension on a blueprint that features an irregular form.
- Solve for an unknown length in a sample drawing of an irregular object using the Pythagorean Theorem.
- Solve for an unknown length in a sample drawing with an irregular object using the Pythagorean Theorem.
- Solve for an unknown length of a cylindrical, symmetrical part.

## Job Roles

## Certifications

NIMS- CNC Milling Programming, Setup, & Operation
- CNC Milling: Programming, Setup, and Operations-FastTrack
- CNC Turning Programming, Setup, & Operation
- CNC Turning: Programming, Setup, and Operations-FastTrack
- Grinding I
- Grinding Skills-FastTrack
- Job Planning, Benchwork, & Layout I
- Job Planning, Benchwork, and Layout-FastTrack
- Measurement, Materials, & Safety I
- Measurement, Materials, and Safety-FastTrack

## Glossary

Vocabulary Term | Definition |
---|---|

angle | A shape formed by two lines that intersect or two rays or line segments sharing a common endpoint. An angle has one vertex and two sides. |

diameter | The distance from one edge of a circle to the opposite edge that passes through the center. The diameter is always twice the length of the radius. |

exponent | A number or symbol that indicates the number of times a digit should be multiplied by itself. For example, if 4² appears in an equation, four should be multiplied by itself once, which equals sixteen. |

hypotenuse | In a right triangle, the side located opposite the right angle. The hypotenuse is always the longest side. |

legs | A side of a right triangle other than the hypotenuse. The legs of the right triangle are represented by the letters a and b in the Pythagorean theorem. |

powers | A mathematical operation indicating how many times a number is multiplied by itself. Three to the power of 2 is 3 times 3, which equals nine. |

Pythagorean theorem | A mathematical rule describing how sides of a right triangle are related. The Pythagorean theorem states that the sum of the square of both sides equals the square of the hypotenuse. |

radius | The distance between a point on a circle and its center. The radius is always half the length of the diameter. |

right triangle | A triangle containing exactly one 90° angle. Right triangles include two other angles that must total 90 degrees. |

root | A value indicating how many times a new, unknown value must be multiplied by itself to equal the stated number or variable. A root is an inverse of a power operation. |

square | A common power in which a number is multiplied by itself once. A square can be expressed by stating the value and then "to the second power" or as the value with the superscript 2 beside it. |

square root | A mathematical function that shows which unknown number is multiplied by itself one time. The square root of 49 is seven. |

symmetrical | A quality in which all the features on either side of a print, part, or other component are identical to the other side. Both sides of a symmetrical part or print have the same dimensions. |

tangent | A line, line segment, or ray that touches a circle at exactly one point. A tangent always forms a right angle with a radius that meets the tangent at the same point on the circle. |

theorem | A statement that must be proven to be true. The Pythagorean theorem has been proven using a step-by-step, logical process. |

V-block | A workholding component that is either magnetic or laminated. V-blocks are designed for grinding angles and holding round, square, or rectangular workpieces. |

vertex | A point where two lines or line segments meet or intersect. A triangle has three vertices. |