# Trigonometry: The Pythagorean Theorem 201

“Trigonometry: The Pythagorean Theorem” provides an explanation of the Pythagorean theorem and how it is used to solve various math problems involving and using right triangles. The class covers the use of powers and roots and the process that is used to solve for unknown dimensions on blueprints.

The Pythagorean theorem is used to solve for the lengths of sides of right triangles. To find missing measurements in a print with a right angle, manufacturers can find or create right triangles and use the Pythagorean theorem. After taking this class, users will be able to use the Pythagorean theorem to calculate missing lengths in right triangles and solve for missing dimensions on various types of blueprints by utilizing right triangles where appropriate.

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## Class Details

Class Name:
Trigonometry: The Pythagorean Theorem 201
Version:
2.0
Difficulty:
Beginner
Number of Lessons:
15
Related 1.0 Class:
Trig: Pythagorean Theorem 205

## 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.

## 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.