Question

Find the value of x. round to the nearest tenth. side length 16. angle 35. view picture below.​

Answer 1

`\displaystyle x \approx 9.2`

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] sinθ = opposite over hypotenuse

Step-by-step explanation:

Step 1: Define

Angle θ = 35°

Opposite leg = x

Hypotenuse = 16

Step 2: Solve for x

1. Substitute in variables [Sine]:
   `\displaystyle sin35^\circ = (x)/(16)`
2. [Multiplication Property of Equality] Isolate x:
   `\displaystyle 16sin35^\circ = x`
3. Rewrite:
   `\displaystyle x = 16sin35^\circ`
4. Evaluate trig:
   `\displaystyle x = 16(0.573576)`
5. Multiply:
   `\displaystyle x = 9.17722`
6. Round:
   `\displaystyle x \approx 9.2`