Question

Calculate the side lengths a and b to two decimal places.

Answer 1

Answer is D

Explanation:

Answer 2

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:
  `(sin(A))/(a) =(sin(B))/(b) =(sin(C))/(c)`

Explanation:

Step 1: Define

AC = b

CB = a

AB = 7

m∠A = 45°

m∠B = 110°

m∠C = ?

Step 2: Find missing ∠

1. Set up equation: m∠C + 45° + 110° = 180°
2. Combine like terms: m∠C + 115° = 180°
3. Isolate unknown: m∠C = 25°

Step 3: Find measure of b

1. Substitute:
   `(sin(25))/(7) =(sin(110))/(b)`
2. Cross-multiply:
   `bsin(25)=7sin(110)`
3. Isolate b:
   `b=(7sin(110))/(sin(25))`
4. Evaluate:
   `b=15.5645`
5. Round:
   `b \approx 15.56`

Step 4: Find measure of a

1. Substitute:
   `(sin(25))/(7) =(sin(45))/(a)`
2. Cross-multiply:
   `asin(25)=7sin(45)`
3. Isolate a:
   `a=(7sin(45))/(sin(25))`
4. Evaluate:
   `a=11.7121`
5. Round:
   `a \approx 11.71`