Trigonometry Review

Legs of a right triangle

the two sides that form the right angle

Angle of depression

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

Angle of elevation

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

Cosine

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

Geometric mean

the mean of n numbers expressed as the n-th root of their product

Inverse cosine

An inverse trigonometric ratio, abbreviated as cosˉ¹. For acute angle A, if cosA=z, then cosˉ¹z=m

Inverse sine

An inverse trigonometric ratio abbreviated as sin-1

Inverse tangent

an inverse trigonometric ratio, abbreviated as tan-1

Law of cosines

a²=b²+c²-2bcCosA

Law of sines

sinA/a=sinB/b=sinC/c

Pythagorean triple

a set of three positive integers that work in the pythagorean theorem

Sine

ratio of the opposite side to the hypotenuse of a right-angled triangle

Tangent

ratio of the opposite to the adjacent side of a right-angled triangle

Trignometric ratio

a ratio of two sides of a right triangle

AA Triangle Similarity Theorem

If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.

SAS Triangle Similarity Theorem

If two sides of one triangle are proportional to the corresponding sides of another triangle and their included angles are congruent, then the triangles are similar.

SSS Triangle Similarity Theorem

If the three sides of one triangle are proportional to the corresponding sides of another triangle, then the triangles are similar.

Corresponding parts of similar triangles

Two triangles are similar if and only if the corresponding sides are in proportion and the corresponding angles are congruent. There are three accepted methods of proving triangles similar: AA, SAS, and SSS.