Question

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

Answer 1

Answer:

$\displaystyle EF \approx 15.9$

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

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]:                                                                    $\displaystyle cos28^\circ = \frac{x}{18}$
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:                                                                                                             $\displaystyle EF \approx 15.9$