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

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

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Answer:

[tex]\displaystyle EF \approx 15.9[/tex]

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: Define

Angle θ = 28°

Adjacent Leg = EF = x

Hypotenuse = DF = 18

Step 2: Solve for x

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

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