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Yanka [14]
2 years ago
7

Find the value of the trig function indicated.

Mathematics
2 answers:
11Alexandr11 [23.1K]2 years ago
7 0

Answer:

Solution given;

In right angled triangle with respect to θ

perpendicular: opposite side: [P]=12

base:adjacent:[b]=8

hypotenuse [h]=?

cosθ=?

According to the Pythagoras law

h²=p²+b²

h²=12²+8²

h=\sqrt{208}

h=4\sqrt{13}

Now

we have

Cos θ=\frac{adjacent}{hypotenuse}

Cos θ=\frac{8}{4\sqrt{13}}

by rationalising it

Cos θ= \frac{2\sqrt{13}}{\sqrt{13}×\sqrt{13}}

Cos θ= \frac{2\sqrt{13}}{13}

is a required answer.

jekas [21]2 years ago
6 0

Answer:

\displaystyle cos\theta = \frac{2\sqrt{13}}{13}

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

  • Multiplication Property of Equality
  • Division Property of Equality
  • Addition Property of Equality
  • Subtraction Property of Equality

<u>Trigonometry</u>

[Right Triangles Only] Pythagorean Theorem: a² + b² = c²

  • a is a leg
  • b is another leg
  • c is the hypotenuse

[Right Triangles Only] SOHCAHTOA

[Right Triangles Only] cosθ = adjacent over hypotenuse

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify variables</em>

<em>a</em> = 8

<em>b</em> = 12

<em>c</em>

<u>Step 2: Solve for </u><em><u>c</u></em>

  1. Substitute in variables [Pythagorean Theorem]:                                          8² + 12² = c²
  2. Evaluate exponents:                                                                                       64 + 144 = c²
  3. Add:                                                                                                                 208 = c²
  4. [Equality Property] Square root both sides:                                                  √208 = c
  5. Rewrite:                                                                                                           c = √208
  6. Simplify:                                                                                                           c = 4√13

<u>Step 3: Define Pt. 2</u>

<em>Identify variables</em>

Angle θ

Adjacent leg = 8

Hypotenuse = 4√13

<u>Step 4: Find</u>

  1. Substitute in variables [Cosine]:                                                                   \displaystyle cos\theta = \frac{8}{4\sqrt{13}}
  2. Rationalize:                                                                                                     \displaystyle cos\theta = \frac{2\sqrt{13}}{13}
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*Given
Money of Phoebe            - 3 times as much as Andy
Money of Andy                - 2 times as much as Polly
Total money of Phoebe,  - <span>£270
</span>    Andy and Polly

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B - Phoebe's money
A - Andy's money
L - Polly's money

1. The money of the Phoebe, Andy, and Polly, when added together would total <span>£270. Thus, 
</span>
                  B + A + L  = <span>£270                     (EQUATION 1)

2. Phoebe has three times as much money as Andy and this is expressed as
  
                  B = 3A

3. Andy has twice as much money as Polly and this is expressed as

                  A = 2L</span>                           (EQUATION 2)
<span>
4. This means that Phoebe has ____ as much money as Polly, 

                 B = 3A
                 B = 3 x (2L)
                 B = 6L                            </span>(EQUATION 3)<span>

This step allows us to eliminate the variables B and A in EQUATION 1 by expressing the equation in terms of Polly's money only. 

5. Substituting B with 6L, and A with 2L, EQUATION 1 becomes, 

                  6L + 2L + L = </span><span>£270
</span>                                9L = <span>£270
</span>                                  L = <span>£30

So, Polly has </span><span>£30. 

6. Substituting L into EQUATIONS 2 and 3 would give us the values for Andy's money and Phoebe's money, respectively. 
</span>
                  A = 2L                           
                  A = 2(£30)
                  A = £60

Andy has £60

                  B = 6L                         
                  B = 6(£30)
                  B = £180

Phoebe has £180

Therefore, Polly's money is £30, Andy's is £60, and Phoebe's is £180.
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