Question

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Answer 1

Answer:

$\displaystyle x = \frac{25\sqrt{2}}{2}$

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

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