Trigonometry: The Pythagorean Theorem 201
Consider the measurements of the right triangle in the image. What is the length of the unknown leg?
22.4362
Consider the measurements of the right triangle in the image. What is the length of the unknown hypotenuse?
31.9001
A right triangle has legs measuring 2.5 inches and 3.2 inches. What is the length of the hypotenuse?
4.06
A right triangle has one leg measuring 3.1 inches and a hypotenuse measuring 7.8 inches. What is the length of the other leg?
7.16
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.
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.
Square Root
A mathematical function that shows which unknown number is multiplied by itself one time. The square root of 49 is seven.
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.
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.
Vertex
A point where two lines or line segments meet or intersect. A triangle has three vertices.
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.
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.
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.
Theorem
A statement that must be proven to be true. The Pythagorean theorem has been proven using a step-by-step, logical process.
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.
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.
TRUE/FALSE: Adding a square form on a blueprint with circles in a V-block problem aids in solving for missing dimensions.
False
TRUE/FALSE: Cylindrical parts on a die punch problem are asymmetrical.
False
TRUE/FALSE: The Pythagorean theorem is used to solve for unknown angles in irregular forms.
False
Which of the following statements is true concerning the Pythagorean theorem? The Pythagorean theorem states that the square of the hypotenuse of a right triangle is:
The sum of the values of the legs squared.
Which statement is true about a right triangle?
The two angles other than the right angle must total 90 degrees.
To form a right triangle on a blueprint in order to solve for an unknown length in an irregular form, what must be true?
The unknown length must be on a line that is tangent to a circle.
Which of the following describes the function of a power?
To indicate the number of times a value is multiplied by itself.
TRUE/FALSE: A line that intersects a radius at the perimeter of a circle and creates a 90° angle is a tangent.
True
TRUE/FALSE: If the length of a radius is known, a related but unknown diameter can be found.
True
TRUE/FALSE: The Pythagorean theorem is used to find a missing dimension on a blueprint with a part that has both curved and straight features.
True
TRUE/FALSE: The Pythagorean theorem is used to find the missing leg in a die punch problem.
True
TRUE/FALSE: The radius in the blueprint of a die punch problem is used to form the hypotenuse of the right triangle.
True
Which of the following equations represents the Pythagorean theorem?
c squared = a squared + b squared
Hypotenuse
In a right triangle, the side located opposite the right angle. The hypotenuse is always the longest side.
Radius
The distance between a point on a circle and its center. The radius is always half the length of the diameter.
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.
Which of the following describes an exponent? An exponent is:
The number that represents how many times a number is multiplied by itself.
What is the defining characteristic of a right triangle?
The presence of one 90 degree angle.
