Glencoe Geometry Chapter 8 Flashcards

Questions and Answers

What is the angle of depression?

The angle formed by a horizontal line and the line of sight to an object below the horizontal line.

What is the angle of elevation?

The angle formed by a horizontal line and the line of sight to an object above the horizontal line.

What is cosine?

The ratio of the adjacent side to the hypotenuse of a right-angled triangle.

What is sine?

The ratio of the opposite side to the hypotenuse of a right-angled triangle. Signup and view all the answers

What is tangent?

The ratio of the opposite side to the adjacent side of a right-angled triangle. Signup and view all the answers

What does solving a triangle involve?

Finding the measures of all of the angles and sides of a triangle. Signup and view all the answers

What is a trigonometric ratio?

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

What is the geometric mean?

The mean of n numbers expressed as the n-th root of their product. Signup and view all the answers

What is Trigonometry?

The mathematics of triangles and trigonometric functions. Signup and view all the answers

What is a Pythagorean triple?

A set of three positive integers that work in the Pythagorean theorem. Signup and view all the answers

What is the Law of Sines?

sinA/a = sinB/b = sinC/c Signup and view all the answers

What is the Law of Cosines?

c² = a² + b² - 2abcosC Signup and view all the answers

Study Notes

Angles and Lines of Sight

Angle of Depression: Formed by a horizontal line and the line of sight to an object below.
Angle of Elevation: Formed by a horizontal line and the line of sight to an object above.

Trigonometric Functions

Cosine: Ratio of the length of the adjacent side to the hypotenuse in a right-angled triangle.
Sine: Ratio of the length of the opposite side to the hypotenuse in a right-angled triangle.
Tangent: Ratio of the opposite side to the adjacent side in a right-angled triangle.

Triangle Properties

Solving a Triangle: Involves finding all angles and side lengths of a triangle.
Trigonometric Ratio: A ratio comparing two sides of a right triangle.

Means and Geometry

Geometric Mean: Calculated as the n-th root of the product of n numbers.
Trigonometry: The branch of mathematics focused on the properties and relationships of triangles and trigonometric functions.

Important Theorems

Pythagorean Triple: A set of three positive integers satisfying the Pythagorean theorem; typically expressed as (a, b, c).
Law of Sines: Relates the ratios of the sides of a triangle to the sines of its angles: sinA/a = sinB/b = sinC/c.
Law of Cosines: Provides a formula for calculating a side of a triangle based on the others and the included angle: c² = a² + b² - 2abcosC.

Description

Test your knowledge of key concepts from Glencoe Geometry Chapter 8 with these flashcards. Learn essential terms like angle of depression, angle of elevation, and cosine, and understand their definitions. Perfect for reviewing and reinforcing your geometry skills.