Question

Solve for X in the triangle. Round your answer to the nearest tenth

Answer 1

`\displaystyle x \approx 9.9`

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] sinθ = opposite over hypotenuse

Explanation:

Step 1: Define

Identify variables

Angle θ = 64°

Opposite Leg = x

Hypotenuse = 11

Step 2: Solve for x

1. Substitute in variables [sine]:
   `\displaystyle sin(64^\circ) = (x)/(11)`
2. [Multiplication Property of Equality] Multiply 11 on both sides:
   `\displaystyle 11sin(64^\circ) = x`
3. Rewrite:
   `\displaystyle x = 11sin(64^\circ)`
4. Evaluate:
   `\displaystyle x = 9.88673`
5. Round:
   `\displaystyle x \approx 9.9`