Question

PQR is a right angled triangle calculate the size of angle marked x

Answer 1

`\displaystyle x \approx 37.4^\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

Explanation:

Step 1: Define

Angle θ = x

Adjacent Leg = 5.8

Hypotenuse = 7.3

Step 2: Solve for x

1. Substitute in variables [Cosine]:
   `\displaystyle cosx^\circ = (5.8)/(7.3)`
2. [Fraction] Divide:
   `\displaystyle cosx^\circ = 0.794521`
3. [Equality Property] Trig inverse:
   `\displaystyle x^\circ = cos^(-1)(0.794521)`
4. Evaluate trig inverse:
   `\displaystyle x = 37.39^\circ`
5. Round:
   `\displaystyle x \approx 37.4^\circ`