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- https://math.libretexts.org/Courses/Prince_Georges_Community_College/MAT_1350%3A_Precalculus_Part_I/10%3A_Further_Applications_of_Trigonometry/10.02%3A_Non-right_Triangles_-_Law_of_CosinesUnfortunately, while the Law of Sines enables us to address many non-right triangle cases, it does not help us with triangles where the known angle is between two known sides, a SAS (side-angle-side) ...Unfortunately, while the Law of Sines enables us to address many non-right triangle cases, it does not help us with triangles where the known angle is between two known sides, a SAS (side-angle-side) triangle, or when all three sides are known, but no angles are known, a SSS (side-side-side) triangle. In this section, we will investigate another tool for solving oblique triangles described by these last two cases.
- https://math.libretexts.org/Courses/Las_Positas_College/Book%3A_College_Algebra/02%3A_Equations_and_Inequalities/2.02%3A_The_Rectangular_Coordinate_Systems_and_GraphsDescartes introduced the components that comprise the Cartesian coordinate system, a grid system having perpendicular axes. Descartes named the horizontal axis the \(x\)-axis and the vertical axis the...Descartes introduced the components that comprise the Cartesian coordinate system, a grid system having perpendicular axes. Descartes named the horizontal axis the \(x\)-axis and the vertical axis the \(y\)-axis. This system, also called the rectangular coordinate system, is based on a two-dimensional plane consisting of the \(x\)-axis and the \(y\)-axis. Perpendicular to each other, the axes divide the plane into four sections. Each section is called a quadrant.
- https://math.libretexts.org/Courses/Chabot_College/Chabot_College_College_Algebra_for_BSTEM/02%3A_Equations_and_Inequalities/2.01%3A_The_Rectangular_Coordinate_Systems_and_GraphsDescartes introduced the components that comprise the Cartesian coordinate system, a grid system having perpendicular axes. Descartes named the horizontal axis the \(x\)-axis and the vertical axis the...Descartes introduced the components that comprise the Cartesian coordinate system, a grid system having perpendicular axes. Descartes named the horizontal axis the \(x\)-axis and the vertical axis the \(y\)-axis. This system, also called the rectangular coordinate system, is based on a two-dimensional plane consisting of the \(x\)-axis and the \(y\)-axis. Perpendicular to each other, the axes divide the plane into four sections. Each section is called a quadrant.
- https://math.libretexts.org/Courses/Chabot_College/Math_in_Society_(Zhang)/02%3A_Geometry/2.01%3A_Basic_Geometric_Concepts_and_FiguresYou use geometric terms in everyday language, often without thinking about it. For example, any time you say “walk along this line” or “watch out, this road quickly angles to the left”, you are using ...You use geometric terms in everyday language, often without thinking about it. For example, any time you say “walk along this line” or “watch out, this road quickly angles to the left”, you are using geometric terms to make sense of the environment around you. In the world of mathematics, each of these geometric terms has a specific definition. It is important to know these definitions—as well as how different figures are constructed—to become familiar with the language of geometry.
- https://math.libretexts.org/Courses/Hawaii_Community_College/Hawaii_Community_College_MA82X_Textbook/03%3A_Math_Models/3.04%3A_Triangles_Rectangles_and_the_Pythagorean_TheoremIn this section we will use some common geometry formulas. We will adapt our problem-solving strategy so that we can solve geometry applications. The geometry formula will name the variables and give ...In this section we will use some common geometry formulas. We will adapt our problem-solving strategy so that we can solve geometry applications. The geometry formula will name the variables and give us the equation to solve. In addition, since these applications will all involve shapes of some sort, most people find it helpful to draw a figure and label it with the given information. We will include this in the first step of the problem solving strategy for geometry applications.
- https://math.libretexts.org/Bookshelves/Algebra/Intermediate_Algebra_(Arnold)/09%3A_Radical_Functions/9.06%3A_The_Pythagorean_TheoremPythagoras was a Greek mathematician and philosopher, born on the island of Samos (ca. 582 BC). He founded a number of schools, one in particular in a town in southern Italy called Crotone, whose memb...Pythagoras was a Greek mathematician and philosopher, born on the island of Samos (ca. 582 BC). He founded a number of schools, one in particular in a town in southern Italy called Crotone, whose members eventually became known as the Pythagoreans. Today, nothing is known of Pythagoras’s writings, perhaps due to the secrecy and silence of the Pythagorean society. However, one of the most famous theorems in all of mathematics does bear his name, the Pythagorean Theorem.
- https://math.libretexts.org/Courses/Borough_of_Manhattan_Community_College/MAT_206_Precalculus/7%3A_Trigonometric_Identities_and_Equations/7.5%3A_Solving_Trigonometric_EquationsIn earlier sections of this chapter, we looked at trigonometric identities. Identities are true for all values in the domain of the variable. In this section, we begin our study of trigonometric equat...In earlier sections of this chapter, we looked at trigonometric identities. Identities are true for all values in the domain of the variable. In this section, we begin our study of trigonometric equations to study real-world scenarios such as the finding the dimensions of the pyramids.
- https://math.libretexts.org/Bookshelves/Algebra/Algebra_and_Trigonometry_1e_(OpenStax)/10%3A_Further_Applications_of_Trigonometry/10.02%3A_Non-right_Triangles_-_Law_of_CosinesUnfortunately, while the Law of Sines enables us to address many non-right triangle cases, it does not help us with triangles where the known angle is between two known sides, a SAS (side-angle-side) ...Unfortunately, while the Law of Sines enables us to address many non-right triangle cases, it does not help us with triangles where the known angle is between two known sides, a SAS (side-angle-side) triangle, or when all three sides are known, but no angles are known, a SSS (side-side-side) triangle. In this section, we will investigate another tool for solving oblique triangles described by these last two cases.
- https://math.libretexts.org/Bookshelves/Algebra/Book%3A_Arithmetic_and_Algebra_(ElHitti_Bonanome_Carley_Tradler_and_Zhou)/02%3A_Appendices/2.04%3A_The_Pythagorean_TheoremThe Pythagorean Theorem relates the lengths of the legs of a right triangle and the hypotenuse.
- https://math.libretexts.org/Bookshelves/Precalculus/Book%3A_Precalculus__An_Investigation_of_Functions_(Lippman_and_Rasmussen)/05%3A_Trigonometric_Functions_of_Angles/5.01%3A_CirclesIf we wanted to find an equation to represent a circle with a radius of r centered at a point ( h , k ), we notice that the distance between any point ( x , y ) on the circle and the center point ...If we wanted to find an equation to represent a circle with a radius of r centered at a point ( h , k ), we notice that the distance between any point ( x , y ) on the circle and the center point is always the same: r.
- https://math.libretexts.org/Courses/Nova_Scotia_Community_College/MATH_1043/07%3A_Geometry/7.04%3A_The_Pythagorean_TheoremPythagoras was a Greek mathematician and philosopher, born on the island of Samos (ca. 582 BC). He founded a number of schools, one in particular in a town in southern Italy called Crotone, whose memb...Pythagoras was a Greek mathematician and philosopher, born on the island of Samos (ca. 582 BC). He founded a number of schools, one in particular in a town in southern Italy called Crotone, whose members eventually became known as the Pythagoreans. Today, nothing is known of Pythagoras’s writings, perhaps due to the secrecy and silence of the Pythagorean society. However, one of the most famous theorems in all of mathematics does bear his name, the Pythagorean Theorem.
