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

Calculate the side lengths a and b to two decimal places.-example-1
User Schwierig
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2 Answers

5 votes

Answer:

Answer is D

Explanation:

User NuSphere
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5 votes

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:
    (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
User Nightograph
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