Answer:
[tex]\displaystyle x \approx 38.2 ^{\circ}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtract Property of Equality
Pre-Calculus
Law of Sines: [tex]\displaystyle \frac{sin(A)}{a} =\frac{sin(B)}{b} =\frac{sin(C)}{c}[/tex]
- A, B, C are angle measures
- a, b, c are leg lengths
Step-by-step explanation:
Step 1: Identify
A = 27°, a = 11
B = x°, b = 15
Step 2: Solve for x
- Substitute [LOS]: [tex]\displaystyle \frac{sin(27^{\circ})}{11} =\frac{sin(x^{\circ})}{15}[/tex]
- Cross-multiply: [tex]\displaystyle 11sin(x^{\circ}) = 15sin(27^{\circ})[/tex]
- Isolate x term: [tex]\displaystyle sin(x^{\circ}) = \frac{15sin(27^{\circ})}{11}[/tex]
- Isolate x: [tex]\displaystyle x = sin^{-1}(\frac{15sin(27)}{11})[/tex]
- Evaluate: [tex]\displaystyle x = 38.2488 ^{\circ}[/tex]
- Round: [tex]\displaystyle x \approx 38.2 ^{\circ}[/tex]
