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Find the value of x.
Round to the nearest tenth.
100°
25
30
х
x = [?]
Law of Cosines : c2 = a + b2 - 2ab cos C

Find The Value Of X Round To The Nearest Tenth 100 25 30 Х X Law Of Cosines C2 A B2 2ab Cos C class=

Sagot :

Space

Answer:

x ≈ 42.3

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

Algebra I

  • Equality Properties

Pre-Calculus

  • Law of Cosines: c² = a² + b² - 2(a)(b)cosC°

Step-by-step explanation:

Step 1: Identify

Leg a = 25

Leg b = 30

C = 100°

Leg c = x

Step 2: Solve for x

  1. Substitute [LOC]:                    x² = 25² + 30² - 2(25)(30)cos100°
  2. Exponents:                              x² = 625 + 900 - 2(25)(30)cos100°
  3. Multiply:                                  x² = 625 + 900 - 1500cos100°
  4. Evaluate:                                 x² = 625 + 900 - 1500(-0.173648)
  5. Multiply:                                  x² = 625 + 900 + 260.472
  6. Add:                                        x² = 1525 + 260.472
  7. Add:                                        x² = 1785.47
  8. Isolate x:                                 x = 42.2548
  9. Round:                                    x ≈ 42.3
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