Question

Find the value of X

PLEASE

Answer 1

x ≈ 18

General Formulas and Concepts:

Pre-Algebra

• Order of Operations: BPEMDAS
• Equality Properties

Trigonometry

Law of Cosines: a^2 = b^2 + c^2 - 2(b)(c)cosA

• a is a side length
• b is a side length
• c is a side length
• A is an angle corresponding with side a

Explanation:

Step 1: Define

a = x

A = 30°

b = 16

c = 30

Step 2: Solve for x

1. Substitute: x² = 16² + 30² - 2(16)(30)cos30°
2. Exponents: x² = 256 + 900 -2(16)(30)cos30°
3. Evaluate: x² = 256 + 900 -2(16)(30)(√3/2)
4. Multiply: x² = 256 + 900 - 480√3
5. Add: x² = 1156 - 480√3
6. Subtract: x² = 324.616
7. Isolate x: x = √324.616
8. Evaluate: x = 18.0171
9. Round: x ≈ 18