Question

Find the value of x. Round the length to the nearest tenth.

33 cm
4.1 cm
4.4 cm
11.3 cm

Answer 1

4.4 cm

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] tanθ = opposite over adjacent

Explanation:

Step 1: Define

Identify variables

Angle θ = 20°

Opposite Leg = x

Adjacent Leg = 12 cm

Step 2: Solve for x

1. Substitute in variables [Tangent]:
   `\displaystyle tan(20^\circ) = (x)/(12)`
2. [Multiplication Property of Equality] Multiply 12 on both sides:
   `\displaystyle 12tan(20^\circ) = x`
3. Rewrite:
   `\displaystyle x = 12tan(20^\circ)`
4. Evaluate:
   `\displaystyle x = 4.36764`
5. Round:
   `\displaystyle x = 4.4`

Answer 2

4.4 =x

Explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp/ adj

tan 20 = x/12

12 tan 20 = x

4.367642811=x

Rounding to the nearest tenth

4.4 =x