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Answer :

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Answer:

[tex]\displaystyle x \approx 11.1[/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] cosθ = adjacent over hypotenuse

Step-by-step explanation:

Step 1: Define

Angle θ = 42°

Adjacent Leg = x

Hypotenuse = 15

Step 2: Solve for x

  1. Substitute in variables [cosine]:                                                                       [tex]\displaystyle cos42^\circ = \frac{x}{15}[/tex]
  2. [Multiplication Property of Equality] Isolate x:                                               [tex]\displaystyle 15cos42^\circ = x[/tex]
  3. Rewrite:                                                                                                            [tex]\displaystyle x = 15cos42^\circ[/tex]
  4. Evaluate:                                                                                                          [tex]\displaystyle x = 11.1472[/tex]
  5. Round:                                                                                                              [tex]\displaystyle x \approx 11.1[/tex]

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