Find the value of x. Round to the nearest tenth.
100°
25
30
х
x = [?]
Law of Cosines : c2 = a + b2 - 2ab cos C

x ≈ 42.3

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Equality Properties

Pre-Calculus

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

Step-by-step explanation:

Step 1: Identify

Leg a = 25

Leg b = 30

C = 100°

Leg c = x

Step 2: Solve for x

Substitute [LOC]:                    x² = 25² + 30² - 2(25)(30)cos100°Exponents:                              x² = 625 + 900 - 2(25)(30)cos100°Multiply:                                  x² = 625 + 900 - 1500cos100°Evaluate:                                 x² = 625 + 900 - 1500(-0.173648)Multiply:                                  x² = 625 + 900 + 260.472Add:                                        x² = 1525 + 260.472Add:                                        x² = 1785.47Isolate x:                                 x = 42.2548Round:                                    x ≈ 42.3