Find the value of x. Round the length to the nearest tenth. 33 cm
4.1 cm
4.4 cm
11.3 cm

4.4 cm

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition 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

Step-by-step explanation:

Step 1: Define

Identify variables

Angle θ = 20°

Opposite Leg = x

Adjacent Leg = 12 cm

Step 2: Solve for x

Substitute in variables [Tangent]:                                                                    [Multiplication Property of Equality] Multiply 12 on both sides:                     Rewrite:                                                                                                             Evaluate:                                                                                                            Round:                                                                                                              

Use pythagorean’s theorem and find the missing side lengths of the two smaller triangles and add them together
13^2 - 12^2 = 5
15^2 - 12^2 = 9
5+9 = 14
14 is the length of each side of the square
14^2 + 14^2 = 19.8
19.8 is the diagonal length of the inside if the square