Question

someone please help

Answer 1

Answer:

$\displaystyle B \approx 36.87^\circ$

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] cosθ = adjacent over hypotenuse

Step-by-step explanation:

Step 1: Identify Variables

Angle θ = B

Adjacent Leg = 4

Hypotenuse = 5

Step 2: Solve for θ

1. Substitute in variables [cosine]:                                                                     $\displaystyle cosB^\circ = \frac{4}{5}$
2. [Equality Property] Trig inverse:                                                                    $\displaystyle B^\circ = cos^{-1}(\frac{4}{5})$
3. Evaluate:                                                                                                            $\displaystyle B = 36.8699^\circ$
4. Round:                                                                                                              $\displaystyle B \approx 36.87^\circ$