Question

Solve for x. Round your answer to the nearest tenth (one decimal place).

Answer 1

`\displaystyle x \approx 6.7`

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

Angle θ = 78°

Adjacent Leg = x

Hypotenuse = 32

Step 2: Solve for x

1. Substitute in variables [cosine]:
   `\displaystyle cos78^\circ = (x)/(32)`
2. [Multiplication Property of Equality] Multiply 32 on both sides:
   `\displaystyle 32cos78^\circ = x`
3. Rewrite:
   `\displaystyle x = 32cos78^\circ`
4. Evaluate:
   `\displaystyle x = 6.65317`
5. Round:
   `\displaystyle x \approx 6.7`