Use the Law of Cosines to find the values of x and y.

x ≈ 41.4°

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Equality Properties

Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtract Property of Equality

Pre-Calculus

Law of Cosines: c² = a² + b² - 2(a)(b)cosC°

Step-by-step explanation:

Step 1: Identify Variables

C° = x°

c = 12

a = 15

b = 18

Step 2: Solve for x

Substitute [LC]:                    12² = 15² + 18² - 2(15)(18)cosx°Exponents:                           144 = 225 + 324 - 2(15)(18)cosx°Add:                                      144 = 549 - 2(15)(18)cosx°Multiply:                                144 = 549 - 540cosx°Isolate x term:                      -405 = -540cosx°Isolate x term:                      3/4 = cosx°Isolate x:                               cos⁻¹(3/4) = x°Evaluate:                               x = 41.4096°Round:                                  x ≈ 41.4°

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