Answer:
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
Step-by-step explanation:
Step 1: Define
a = x
A = 30°
b = 16
c = 30
Step 2: Solve for x
- Substitute: x² = 16² + 30² - 2(16)(30)cos30°
- Exponents: x² = 256 + 900 -2(16)(30)cos30°
- Evaluate: x² = 256 + 900 -2(16)(30)(√3/2)
- Multiply: x² = 256 + 900 - 480√3
- Add: x² = 1156 - 480√3
- Subtract: x² = 324.616
- Isolate x: x = √324.616
- Evaluate: x = 18.0171
- Round: x ≈ 18
