Respuesta :

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Answer:

[tex]\displaystyle \theta \approx 36.4[/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

  • Multiplication Property of Equality
  • Division Property of Equality
  • Addition Property of Equality
  • Subtraction Property of Equality

Trigonometry

  • [Right Triangles Only] SOHCAHTOA
  • [Right Triangles Only] tanθ = opposite over adjacent
  • Inverse Trig

Step-by-step explanation:

Step 1: Define

Identify variables

Angle θ

Opposite Leg = 31

Adjacent Leg = 42

Step 2: Find Angle

  1. Substitute in variables [tangent]:                                                                    [tex]\displaystyle tan(\theta) = \frac{31}{42}[/tex]
  2. Inverse Trig:                                                                                                      [tex]\displaystyle \theta = tan^{-1}(\frac{31}{42})[/tex]
  3. Evaluate:                                                                                                           [tex]\displaystyle \theta = 36.4309[/tex]
  4. Round:                                                                                                               [tex]\displaystyle \theta \approx 36.4[/tex]

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