Question

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Answer 1

`\displaystyle x = (25√(2))/(2)`

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

Explanation:

Step 1: Define

Identify variables

Angle θ = 45°

Adjacent Leg = 25

Hypotenuse = x

Step 2: Solve for x

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