Question

Find the measure of "theta". Round all answers to the nearest tenth.

Answer 1

`\displaystyle \theta \approx 36.4`

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
• Inverse Trig

Explanation:

Step 1: Define

Identify variables

Angle θ

Opposite Leg = 31

Adjacent Leg = 42

Step 2: Find Angle

1. Substitute in variables [tangent]:
   `\displaystyle tan(\theta) = (31)/(42)`
2. Inverse Trig:
   `\displaystyle \theta = tan^(-1)((31)/(42))`
3. Evaluate:
   `\displaystyle \theta = 36.4309`
4. Round:
   `\displaystyle \theta \approx 36.4`