Geometry Chapter 8 Vocabulary Flashcards

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Questions and Answers

What is the geometric mean?

The average of two numbers

The product of two numbers

The positive square root of two numbers' products (correct)

The sum of two numbers

What is a Pythagorean triple?

A set of three nonzero whole numbers a, b, and c, such that a^2 + b^2 = c^2.

What does cosine represent in right triangle trigonometry?

Adj/hyp

What does sine represent in right triangle trigonometry?

Opp/hyp Signup and view all the answers

What does tangent represent in right triangle trigonometry?

Opp/adj Signup and view all the answers

What is a trigonometric ratio?

The ratio of the lengths of two sides of a right triangle. Signup and view all the answers

What does the term 'trigonometry' mean?

Trigon, meaning triangle, and metron, meaning measure. Signup and view all the answers

What is the inverse cosine?

cos-1 Signup and view all the answers

What is the inverse sine?

sin-1 Signup and view all the answers

What is the inverse tangent?

tan-1 Signup and view all the answers

What is the angle of elevation?

The horizontal line and line of sight above the horizontal line. Signup and view all the answers

What is the angle of depression?

The horizontal line and line of sight below the horizontal line. Signup and view all the answers

What is the Law of Sines used for?

To find side lengths and angle measures for any triangle (AAS or ASA). Signup and view all the answers

What is the Law of Cosines used for?

To solve a triangle with the measures of two sides and the included angle (SAS). Signup and view all the answers

What does magnitude refer to in vector terms?

The length of a vector from its original point to its terminal point. Signup and view all the answers

How is direction expressed in vector analysis?

As the angle it forms with the horizontal or as a measurement between 0 & 90 east or west of the north-south line. Signup and view all the answers

What defines a vector?

Describes the magnitude and direction of the quantity. Signup and view all the answers

What is a resultant vector?

The sum of two or more vectors is a single vector. Signup and view all the answers

What is meant by standard position in terms of vectors?

When a vector's initial point is at the origin. Signup and view all the answers

What is component form of a vector?

To describe a vector with an initial point; (x,y). Signup and view all the answers

Study Notes

Geometry Chapter 8 Vocabulary

Geometric Mean: The positive square root of the product of two numbers, often used in proportions and averages.
Pythagorean Triple: A set of three positive integers ( a, b, c ) that satisfy the condition ( a^2 + b^2 = c^2 ), forming a right triangle.
Cosine: A trigonometric function defined as the ratio of the length of the adjacent side to the hypotenuse in a right triangle, represented as ( \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} ).
Sine: A trigonometric function defined as the ratio of the length of the opposite side to the hypotenuse, expressed as ( \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} ).
Tangent: A trigonometric function representing the ratio of the length of the opposite side to the adjacent side, written as ( \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} ).
Trigonometric Ratio: The ratio of the lengths of two sides of a right triangle, fundamental in trigonometric applications.
Trigonometry: Derived from "trigon" (triangle) and "metron" (measure), it is the mathematical study of relationships involving angles and side lengths in triangles.
Inverse Cosine: The function that determines the angle whose cosine is a given value, denoted as ( \cos^{-1} ).
Inverse Sine: The function that determines the angle whose sine is a given value, denoted as ( \sin^{-1} ).
Inverse Tangent: The function that determines the angle whose tangent is a given value, denoted as ( \tan^{-1} ).
Angle of Elevation: The angle formed between a horizontal line and a line of sight extending upward from the horizontal.
Angle of Depression: The angle formed between a horizontal line and a line of sight extending downward from the horizontal.
Law of Sines: A mathematical rule used to find unknown side lengths and angle measures in any triangle, applicable with Angle-Angle-Side (AAS) or Angle-Side-Angle (ASA) configurations.
Law of Cosines: A formula used to solve triangles when two sides and the included angle (Side-Angle-Side, SAS) are known, providing relationships between side lengths and angles.
Magnitude: Refers to the length of a vector, measured as the distance from its initial point to its terminal point.
Direction: The orientation of a vector, represented by the angle it forms with the horizontal or the measurement in degrees (0° to 90°) east or west of the north-south line.
Vector: A quantity described by both magnitude and direction, essential for representing variables in physics and mathematics.
Resultant: The single vector that results from the vector addition of two or more vectors, encapsulating their combined effect.
Standard Position: A term describing a vector when its initial point is located at the origin of a coordinate system.
Component Form: A way to express a vector using its initial point and final point, typically in the format (x, y), indicating its horizontal and vertical components.

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Test your knowledge of key terms in Geometry Chapter 8 with these flashcards. Each card highlights important concepts such as geometric mean, pythagorean triples, and trigonometric ratios. Perfect for students looking to enhance their understanding of geometry vocabulary.