Question

How do i solve this?​

Answer 1

m∠R = 60°

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

Explanation:

Step 1: Identify

Angle θ = ∠R

Opposite Leg of ∠R = 10√3

Hypotenuse = 20

Step 2: Solve

1. Substitute in variables [sine]:
   `\displaystyle sin(R^\circ) = (10√(3))/(20)`
2. [Equality Property] Trig inverse:
   `\displaystyle R^\circ = sin^(-1)((10√(3))/(20))`
3. Evaluate trig:
   `\displaystyle R = 60^\circ`