Answer:
D. a = 11.71 and b = 15.56
General Formulas and Concepts:
Pre-Algebra
- Order of Operations: BPEMDAS
- Equality Properties
Trigonometry
- All angles in a triangle add up to 180°
Pre-Calculus
- Law of Sines: [tex]\frac{sin(A)}{a} =\frac{sin(B)}{b} =\frac{sin(C)}{c}[/tex]
Step-by-step explanation:
Step 1: Define
AC = b
CB = a
AB = 7
m∠A = 45°
m∠B = 110°
m∠C = ?
Step 2: Find missing ∠
- Set up equation: m∠C + 45° + 110° = 180°
- Combine like terms: m∠C + 115° = 180°
- Isolate unknown: m∠C = 25°
Step 3: Find measure of b
- Substitute: [tex]\frac{sin(25)}{7} =\frac{sin(110)}{b}[/tex]
- Cross-multiply: [tex]bsin(25)=7sin(110)[/tex]
- Isolate b: [tex]b=\frac{7sin(110)}{sin(25)}[/tex]
- Evaluate: [tex]b=15.5645[/tex]
- Round: [tex]b \approx 15.56[/tex]
Step 4: Find measure of a
- Substitute: [tex]\frac{sin(25)}{7} =\frac{sin(45)}{a}[/tex]
- Cross-multiply: [tex]asin(25)=7sin(45)[/tex]
- Isolate a: [tex]a=\frac{7sin(45)}{sin(25)}[/tex]
- Evaluate: [tex]a=11.7121[/tex]
- Round: [tex]a \approx 11.71[/tex]
