Answer :

Answer:

[tex]b \approx 4.6[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

Equality Properties

Pre-Calculus

  • Law of Sines: [tex]\frac{sin(A)}{a} = \frac{sin(B)}{b}[/tex]

Step-by-step explanation:

Step 1: Define

A = 50°

B = 62°

a = 4

Step 2: Solve for b

  1. Substitute [LOS]: [tex]\frac{sin(50)}{4} = \frac{sin(62)}{b}[/tex]
  2. Cross-multiply: [tex]bsin(50) = 4sin(62)[/tex]
  3. Isolate b: [tex]b = \frac{4sin(62)}{sin(50)}[/tex]
  4. Evaluate: [tex]b = 4.61042[/tex]
  5. Round: [tex]b \approx 4.6[/tex]

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Rewritten by : Barada

Final answer:

In this trigonometry problem, you can find the length of side 'b' in a triangle with known angles and one side length using the Law of Sines. The calculated length of 'b', rounded to the nearest tenth, is approximately 4.6.

Explanation:

The provided question refers to the Law of Sines in trigonometry, where the ratios of the lengths of the sides of a triangle to the sines of their opposite angles are constant. So, if A = 50 degrees, a = 4, and B = 62 degrees, you can find the length of side 'b' using this formula: a/sinA = b/sinB. Plugging in the given values, you have:
4 / sin(50) = b / sin(62). Solving for 'b', you get: b = 4 * sin(62) / sin(50). Calculating this gives you b ≈ 4.6 (rounded to the nearest tenth).

Learn more about Law of Sines here:

https://brainly.com/question/12652434

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