Question

Enter the length of PQ to the nearest tenth.​

Answer 1

`\displaystyle PQ \approx 5.2`

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: Identify

Angle θ = 55°

Adjacent Leg = PQ

Hypotenuse = 9

Step 2: Solve

1. Substitute in variables [cosine]:
   `\displaystyle cos55^\circ = (PQ)/(9)`
2. [Multiplication Property of Equality] Isolate PQ:
   `\displaystyle 9cos55^\circ = PQ`
3. Evaluate:
   `\displaystyle 5.16219 = PQ`
4. Rewrite:
   `\displaystyle PQ = 5.16219`
5. Round:
   `\displaystyle PQ \approx 5.2`