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Answer:

[tex]\displaystyle x = \frac{25\sqrt{2}}{2}[/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

Identify variables

Angle θ = 45°

Adjacent Leg = 25

Hypotenuse = x

Step 2: Solve for x

  1. Substitute in variables [cosine]:                                                                   [tex]\displaystyle cos(45^\circ) = \frac{x}{25}[/tex]
  2. [Multiplication Property of Equality] Multiply 25 on both sides:                 [tex]\displaystyle 25cos(45^\circ) = x[/tex]
  3. Rewrite:                                                                                                         [tex]\displaystyle x = 25cos(45^\circ)[/tex]
  4. Evaluate:                                                                                                         [tex]\displaystyle x = \frac{25\sqrt{2}}{2}[/tex]
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