Question

DEF is a right angled triangle calculate the length of EF correct to 3 sigificant figures

Answer 1

`\displaystyle EF \approx 15.9`

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 = 28°

Adjacent Leg = EF = x

Hypotenuse = DF = 18

Step 2: Solve for x

1. Substitute in variables [Cosine]:
   `\displaystyle cos28^\circ = (x)/(18)`
2. [Multiplication Property of Equality] Multiply 18 on both sides:
   `\displaystyle 18cos28^\circ = x`
3. Evaluate trig:
   `\displaystyle 18(0.882948) = x`
4. Multiply:
   `\displaystyle 15.8931 = x`
5. Rewrite:
   `\displaystyle EF = 15.8931`
6. Round:
   `\displaystyle EF \approx 15.9`