Chapter 9 Extension - Law of Sines and Law of Cosines

angle

A figure formed by two rays with a common endpoint

trigonometric ratio

A ratio of the lengths of two sides in a right triangle

included angle

The angle of a triangle that is formed in between two given sides

side

a line segment formed between two vertices of a polygon

Law of Cosines

a mathematical law that can be used to find missing angle measures or side lengths in a triangle

Law of Sines

a mathematical law that can be used to find missing side lengths and angle measures in a triangle

oblique triangle

a non-right triangle

altitude

a perpendicular segment from a vertex to the line containing the opposite side of a polygon

inverse trigonometric ratio

a ratio that finds the measure of an angle in a right triangle when two of the three side lengths are known.

non-included side

a side that is not located in between two angles of a triangle

sine ratio

a trigonometric ratio that compares the opposite leg of a given angle and the hypotenuse of a right triangle

SIde-Side-Side (SSS)

all three side lengths are given in a triangle; used for Law of Cosines

non-included angle

an angle of a triangle that is not between two given sides

solving a triangle

find all unknown side lengths and angle measures of a triangle

Angle-Side-Angle (ASA)

the measures of two angles and one included side length are given in a triangle; used for Law of Sines

Angle-Angle-Side (AAS)

the measures of two angles and one non-included side length are given in a triangle; used for the Law of Sines

included side

the side located between two consecutive angles of a polygon

Side-Angle-Side (SAS)

two sides lengths and the included angle measure are given for a triangle; used for Law of Cosines