Question

Find the value of x.

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

Answer 1

x ≈ 42.3

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
6. Addition
7. Subtraction

• Left to Right

Algebra I

• Equality Properties

Pre-Calculus

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

Explanation:

Step 1: Identify

Leg a = 25

Leg b = 30

C = 100°

Leg c = x

Step 2: Solve for x

1. Substitute [LOC]: x² = 25² + 30² - 2(25)(30)cos100°
2. Exponents: x² = 625 + 900 - 2(25)(30)cos100°
3. Multiply: x² = 625 + 900 - 1500cos100°
4. Evaluate: x² = 625 + 900 - 1500(-0.173648)
5. Multiply: x² = 625 + 900 + 260.472
6. Add: x² = 1525 + 260.472
7. Add: x² = 1785.47
8. Isolate x: x = 42.2548
9. Round: x ≈ 42.3