Sem. 1 Unit 4 Trigonometry – Flashcards

the ratios of the lengths of the sides of a right triangle. The three basic trigonometric ratios are sine, cosine, and tangent.

in a right triangle, the ratio of the length of the angle's opposite leg to the length of the hypotenuse. The abbreviation is sin.

in a right triangle, the ratio of the length of the angle's adjacent leg to the length of the hypotenuse. Its abbreviation is cos.

in a right triangle, the ratio of the angle's opposite leg to the length of the adjacent leg. The abbreviation is tan.

this law is valid for any triangle and can be viewed as a generalization of the Pythagorean theorem. Given a triangle with angles A, B, and C with corresponding side lengths a, b, c, then c^2 + a^2 + b^2 - 2abcos(C).

an acronym for "side-angle-side." These types of problems give you the length of two sides in a triangle and the measure of the angle between those two sides. They can be solved using the law of cosines.

an acronym for "side-side-side." These types of problems give you the length of all three sides. They can be solved using the law of cosines.

this law is valid for any triangle. Given a triangle with angles A, B, and C with corresponding side lengths a, b, c, then sinA/a = sinB/b = sinC/c

an acronym for "angle-side-angle." These types of problems give you the measure of two angles in a triangle and the length of the side between those two angles. They can be solved using the law of sines.

an acronym for "side-angle-angle." These types of problems give you the measure of two angles in a triangle and the length of one of the sides (but not the one between the two angles). They can be solved using the law of sines.

a method of finding the location of an object based on measurements made from two other locations. The law of sines can be used to solve triangulation problems.

If a given triangle can be solved (uniquely) using the law of cosines or sines, then that means that there is only one triangle with the given properties. In other words, any other triangle sharing the same properties will be congruent.

if there were two noncongruent triangles with the same given data, then there is no hope of being able to solve the triangle since there is more than one possible answer!