Question

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

Answer 1

x ≈ 41.4°

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

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°

Explanation:

Step 1: Identify Variables

C° = x°

c = 12

a = 15

b = 18

Step 2: Solve for x

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