Question

What is the value of x to the nearest
tenth?

Answer 1

C. 17.6

Explanation:

tan(40) = x/21

(21) tan(40) = x/21 (21)

21 * tan(40) = x

17.6 = x

Answer 2

C. 17.6

General Formulas and Concepts:

Math

• Rounding

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] tanθ = opposite over adjacent

Explanation:

Step 1: Identify Variables

Angle θ = 40°

Opposite Leg = x

Adjacent Leg = 21

Step 2: Solve for x

1. Substitute in variables [tangent]:
   `\displaystyle tan(40^\circ) = (x)/(21)`
2. [Multiplication Property of Equality] Isolate x:
   `\displaystyle 21tan(40^\circ) = x`
3. Rewrite:
   `\displaystyle x = 21tan(40^\circ)`
4. Evaluate:
   `\displaystyle x = 17.6211`
5. Round:
   `\displaystyle x \approx 17.6`