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Andrei [34K]
2 years ago
15

Solve the right angle trig problem.

Mathematics
1 answer:
iris [78.8K]2 years ago
7 0

Answer:

x = 53.6588°

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

Equality Properties

<u>Trigonometry</u>

  • [Right Triangles Only] SOHCAHTOA
  • [Right Triangles Only] cos∅ = adjacent over hypotenuse

Step-by-step explanation:

<u>Step 1: Define</u>

We are given a right triangle. We can use trig to find the missing angle.

<u>Step 2: Identify Variables</u>

<em>POV from angle x</em>

Angle = <em>x</em>

Adjacent = 16

Hypotenuse = 27

<u>Step 3: Solve for </u><em><u>x</u></em>

  1. Substitute:                    cosx° = 16/27
  2. Inverse:                         x° = cos⁻¹(16/27)
  3. Evaluate:                       x = 53.6588°
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Divide by 2\pi on either sides to isolate r³
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\sqrt[3]{216} = \sqrt[3]{r^3}
6 = r
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S.A = 2\pir² + \pir²
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       =2\pi × 36 + 36\pi
       = 72\pi + 36\pi
       = 108\pi units²  (in terms of \pi)
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Find the angle measures. Justify your responses.
MatroZZZ [7]

Answer:

m∠3 = 2x - 10° and m∠6 = 3x + 20

m∠3 = 58°          ;    m ∠6 = 122°

Step-by-step explanation:

a ║ b

m∠2 = m∠6                     If ║ cut by a transversal, then corresponding angles

                                         are ≅ and =

m∠7 = m∠3                   If ║ cut by a transversal, then corresponding angles

                                       are ≅ and =

m∠2 = 3x + 20              Given

m∠7 = 2x - 10                 Given    

m∠6 + m∠3 = 180°         If ║ cut by a transversal, then each pair of same-side

                                       interior angles (also called consecutive interior angles

                                       are supplementary (sum = 180°) .    

3x + 20 + 2x - 10 = 180°

5x + 10 = 180°

5x = 170°

x = 34°

Answer:   m∠3 = 2x - 10° and m∠6 = 3x + 20

                m∠3 = 2(34) - 10  ;    m∠6 = 3(34) + 20

                 m∠3 = 58°          ;    m ∠6 = 122°

                                 

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