Find the value of the trig function indicated.

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to Right  

Equality Properties

Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of Equality

Trigonometry

[Right Triangles Only] Pythagorean Theorem: a² + b² = c²

a is a legb is another legc is the hypotenuse

[Right Triangles Only] SOHCAHTOA

[Right Triangles Only] cosθ = adjacent over hypotenuse

Step-by-step explanation:

Step 1: Define

Identify variables

a = 8

b = 12

c

Step 2: Solve for c

Substitute in variables [Pythagorean Theorem]:                                          8² + 12² = c²Evaluate exponents:                                                                                       64 + 144 = c²Add:                                                                                                                 208 = c²[Equality Property] Square root both sides:                                                  √208 = cRewrite:                                                                                                           c = √208Simplify:                                                                                                           c = 4√13

Step 3: Define Pt. 2

Identify variables

Angle θ

Adjacent leg = 8

Hypotenuse = 4√13

Step 4: Find

Substitute in variables [Cosine]:                                                                   Rationalize: